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This paper presents a real-time solution method of the maximum divert trajectory optimization problem for planetary landing. In mid-course, the vehicle is to abort and retarget to a landing site as far from the nominal as physically possible. The divert trajectory must satisfy velocity constraints in the range and cross range directions and a total speed constraint. The thrust magnitude is bounded above and below so that once on, the engine cannot be turned off. Because this constraint is not convex, it is relaxed to a convex constraint and lossless convexification is proved. A transformation of variables is introduced in the nonlinear dynamics and an approximation is made so that the problem becomes a second-order cone problem, which can be solved to global optimality in polynomial time whenever a feasible solution exists. A number of examples are solved to illustrate the effectiveness and efficiency of the solution method. [ABSTRACT FROM AUTHOR]

The design of sparse array which is able to achieve good performance of beam-pattern satisfying the minimum peak sidelobe level (PSL) with the number of sensors as few as possible is a research area of increasing interest. This paper presents a method for planar optimization with sensor selection via convex optimization in condition of constrained beam-pattern. In the optimization procedure, the solution algorithm is based on convex optimization including a reweighted l- norm minimization. The objective is the minimum of the number of sensors and the PSL. Sparse array is obtained by removing those sensors with weights equal to zero or approximately equal to zero. In this paper, we also give the optimization algorithm respectively by row, column and the intersection on the basis of the linear array optimization. Numerical results are included, which illustrate the optimum method for planar arrays overall performs better than the other methods presented above for sensor selection. [ABSTRACT FROM AUTHOR]

In this paper, some properties of linear functionals are studied, which are used in functional analysis, optimization theory, numerical analysis, approximation theory, various applications, etc. [ABSTRACT FROM AUTHOR]

In this paper, a new method is proposed to promote the efficiency and accuracy of nonlinear interval-based programming (NIP) based on approximation models and a local-densifying method. In conventional NIP methods, searching for the response bounds of objective and constraints are required at each iteration step, which forms a nested optimization and leads to extremely low efficiency. In order to reduce the computational cost, approximation models based on radial basis functions (RBF) are used to replace the actual computational models. A local-densifying method is suggested to guarantee the accuracy of the approximation models by reconstructing them with densified samples in iterations. Thus, through a sequence of optimization processes, an optimal result with fine accuracy can be finally achieved. Two numerical examples are used to test the effectiveness of the present method, and it is then applied to a practical engineering problem. [ABSTRACT FROM AUTHOR]

The paper discusses several versions of the method of shortest residuals, a specific variant of the conjugate gradient algorithm, first introduced by Lemaréchal and Wolfe and discussed by Hestenes in a quadratic case. In the paper we analyze the global convergence of the versions considered. Numerical comparison of these versions of the method of shortest residuals and an implementation of a standard Polak–Ribière conjugate gradient algorithm is also provided. It supports the claim that the method of shortest residuals is a viable technique, competitive to other conjugate gradient algorithms. [ABSTRACT FROM AUTHOR]

Fast and accurate simulation of the electromagnetic field around frequency selective surfaces (FSSs) are needed for the design and optimization of devices based on the use of FSSs. The authors recently published a computationally efficient calculation method for the analysis of FSSs where the current distribution in the conducting parts are locally approximated by currents associated to electromagnetic waves propagating perpendicularly to the surface of the FSS. In this paper, an improved version of this method is presented. Here, in addition to the described assumption, local plane wave distribution of the current density is imposed also with respect to that surfaces being perpendicular to the surface of the FSS. By this modification, the error of the described calculations becomes very small in a very broad frequency range while the computational burden remains low, consequently the method can be advantageously applied for the solution of design and optimization problems. [ABSTRACT FROM PUBLISHER]

A typical interpolation strategy for line segments consists of a transition scheme, a Look-ahead ACC/DEC scheduling, and an interpolation algorithm. In these three parts, the main computation occurs in the first and second part. Some research work has been carried out to decrease the computation in the previous literatures, but these methods occupy a lot of computing resources for the optimization process during the calculation of transition curve parameters and feed rates. Consequently, the computational efficiency of interpolation strategy is greatly reduced. To deal with the issue, a real-time interpolation strategy is proposed in this paper. In the transition scheme, a Bézier curve is utilized to smooth the line segments. Based on the relationship among the approximation error, the approximation radius, and the transition curve, the curve can be directly generated when the approximation error is given. In the ACC/DEC scheduling, a 3-segment feed rate profile with jerk continuity is constructed. Meanwhile, a Look-ahead planning based on Backward Scanning and Forward Revision (BSFR) algorithm is utilized to eliminate redundant computation. Compared with Zhao’s and Shi’s strategy, the proposed strategy has the merits of C2 and G2 continuity for the tool path, jerk continuity for the tool movement, and distinguished real-time performance for interpolation. The experiments of 3D pentagram and 2D butterfly are carried out with different strategies and their results demonstrate that the interpolation efficiency can be greatly improved with the proposed strategy. [ABSTRACT FROM AUTHOR]

The limited memory BFGS method (L-BFGS) is an adaptation of the BFGS method for large-scale unconstrained optimization. However, The L-BFGS method need not converge for nonconvex objective functions and it is inefficient on highly ill-conditioned problems. In this paper, we proposed a regularization strategy on the L-BFGS method, where the used regularization parameter may play a compensation role in some sense when the condition number of Hessian approximation tends to become ill-conditioned. Then we proposed a regularized L-BFGS method and established its global convergence even when the objective function is nonconvex. Numerical results show that the proposed method is efficient. [ABSTRACT FROM AUTHOR]

The general methodology of the interpolation theory of potential fields (gravity and magnetic anomalies), and, primarily, the three fundamental ideas underlying this methodology-(I) approximation, (II) linearization, and (III) optimization-are the matter of the utmost importance. The rationale of these ideas and the ways of their practical implementation are discussed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new interior-point method, which is based on an extension of the ideas of self-scaled optimization to the general cases. We suggest using the primal correction process to find a scaling point. This point is used to compute a strictly feasible primal–dual pair by simple projection. Then, we define an affine-scaling direction and perform a prediction step. This is the only moment when the dual barrier is used. Thus, we need only to compute its value, which can even be done approximately. In the second part of the paper, we develop a 4n-self-concordant barrier for an n-dimensional p-cone, which can be used for numerical testing of the proposed technique. [ABSTRACT FROM PUBLISHER]

This paper investigates optimal portfolio strategies in a market with partial information on the drift. The drift is modelled as a function of a continuous-time Markov chain with finitely many states which is not directly observable. Information on the drift is obtained from the observation of stock prices. Moreover, expert opinions in the form of signals at random discrete time points are included in the analysis. We derive the filtering equation for the return process and incorporate the filter into the state variables of the optimization problem. This problem is studied with dynamic programming methods. In particular, we propose a policy improvement method to obtain computable approximations of the optimal strategy. Numerical results are presented at the end. [ABSTRACT FROM AUTHOR]

This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just On. Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new technique based on cubic exponential spline functions for computing approximations to the solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and four and gives approximations which are better than those produced by other collocation, finite difference and spline methods. Numerical evidence is presented to illustrate the applicability of the new methods. [ABSTRACT FROM AUTHOR]

This paper presents two multi-material interpolation schemes as direct generalizations of the well-known SIMP and RAMP material interpolation schemes originally developed for isotropic mixtures of two isotropic material phases. The new interpolation schemes provide generally applicable interpolation schemes between an arbitrary number of pre-defined materials with given (anisotropic) properties. The method relies on a large number of sparse linear constraints to enforce the selection of at most one material in each design subdomain. Topology and multi-material optimization is formulated within a unified parametrization. [ABSTRACT FROM AUTHOR]

In this paper, testing procedures based on double-sampling are proposed that yield gains in terms of power for the tests of General Linear Hypotheses. The distribution of a test statistic, involving both the measurements of the outcome on the smaller sample and of the covariates on the wider sample, is first derived. Then, approximations are provided in order to allow for a formal comparison between the powers of double-sampling and single-sampling strategies. Furthermore, it is shown how to allocate the measurements of the outcome and the covariates in order to maximize the power of the tests for a given experimental cost. [ABSTRACT FROM AUTHOR]

Several risk management and exotic option pricing models have been proposed in the literature which may price European options correctly. A prerequisite of these models is the interpolation of the market implied volatilities or the European option price function. However, the no-arbitrage principle places shape restrictions on the option price function. In this paper, an interpolation method is developed to preserve the shape of the option price function. The interpolation is optimal in terms of minimizing the distance between the implied risk-neutral density and the prior approximation function in L2-norm, which is important when only a few observations are available. We reformulate the problem into a system of semismooth equations so that it can be solved efficiently. [ABSTRACT FROM AUTHOR]

In this paper, a generalized projection quasi-Newton method with inexact line search is proposed for the nonlinear optimization problem with linear constraints. The projection and quasi-Newton technique are used to determine the search direction at each iteration. It is proved that the method has properties of global convergence and superlinear convergence rate under some suitable assumptions. [ABSTRACT FROM AUTHOR]

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled, the dual decomposition scheme involves local parallel subgradient calculations and a global subgradient update performed by a master node. In this paper, we propose a consensus-based dual decomposition to remove the need for such a master node and still enable the computing nodes to generate an approximate dual solution for the underlying convex optimization problem. In addition, we provide a primal recovery mechanism to allow the nodes to have access to approximate near-optimal primal solutions. Our scheme is based on a constant stepsize choice, and the dual and primal objective convergence are achieved up to a bounded error floor dependent on the stepsize and on the number of consensus steps among the nodes. [ABSTRACT FROM AUTHOR]

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of the coordinate descent approach, together with variants and extensions and their convergence properties, mostly with reference to convex objectives. We pay particular attention to a certain problem structure that arises frequently in machine learning applications, showing that efficient implementations of accelerated coordinate descent algorithms are possible for problems of this type. We also present some parallel variants and discuss their convergence properties under several models of parallel execution. [ABSTRACT FROM AUTHOR]

In this paper, we study a semi-infinite programming (SIP) problem with a convex set constraint. Using the value function of the lower level problem, we reformulate SIP problem as a nonsmooth optimization problem. Using the theory of nonsmooth Lagrange multiplier rules and Danskin's theorem, we present constraint qualifications and necessary optimality conditions. We propose a new numerical method for solving the problem. The novelty of our numerical method is to use the integral entropy function to approximate the value function and then solve SIP by the smoothing projected gradient method. Moreover we study the relationships between the approximating problems and the original SIP problem. We derive error bounds between the integral entropy function and the value function, and between locally optimal solutions of the smoothing problem and those for the original problem. Using certain second order sufficient conditions, we derive some estimates for locally optimal solutions of problem. Numerical experiments show that the algorithm is efficient for solving SIP. [ABSTRACT FROM AUTHOR]

In this paper, time-delay control systems with quadratic performance are solved by applying the least square method on the Bezier control points. The approximation process is done in two steps. First, the time interval is divided into $$2k$$ subintervals, then in each subinterval the trajectory and control functions are approximated by the Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree $$n$$ and determined the Bezier curves on any subinterval by $$n+1$$ control points. By considering a least square optimization problem, the control points can be found, then the Bezier curves that approximate the action of control and trajectory can be computed as well. Some numerical examples are given to verify the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

We study optimization problems with value-at-risk (VaR) constraints. Because it lacks subadditivity, VaR is not a coherent risk measure and does not necessarily preserve the convexity. Thus, the problems we consider are typically not provably convex. As such, the conditional value-at-risk (CVaR) approximation is often used to handle such problems. Even though the CVaR approximation is known as the best convex conservative approximation, it sometimes leads to solutions with poor performance. In this paper, we investigate the CVaR approximation from a different perspective and demonstrate what is lost in this approximation. We then show that the lost part of this approximation can be remedied using a sequential convex approximation approach, in which each iteration only requires solving a CVaR-like approximation via certain Monte Carlo techniques. We show that the solution found by this approach generally makes the VaR constraints binding and is guaranteed to be better than the solution found by the CVaR approximation and moreover is empirically often globally optimal for the target problem. The numerical experiments show the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

In this paper, a new nonmonotone inexact line search rule is proposed and applied to the trust region method for unconstrained optimization problems. In our line search rule, the current nonmonotone term is a convex combination of the previous nonmonotone term and the current objective function value, instead of the current objective function value . We can obtain a larger stepsize in each line search procedure and possess nonmonotonicity when incorporating the nonmonotone term into the trust region method. Unlike the traditional trust region method, the algorithm avoids resolving the subproblem if a trial step is not accepted. Under suitable conditions, global convergence is established. Numerical results show that the new method is effective for solving unconstrained optimization problems. [ABSTRACT FROM AUTHOR]

This paper studies a regularization approach for an inverse problem of estimating a spatially-and-temporally dependent Robin coefficient arising in the analysis of convective heat transfer. The parameter-to-state map is analyzed, especially a differentiability result is established. A regularization approach is proposed, and the properties, e.g., existence and optimality system, of the functional are investigated. A finite element method is adopted for discretizing the continuous optimization problem, and the convergence of the finite element approximations as the mesh size and temporal step size tend to zero is established. Numerical results by the conjugate gradient method for one- and two-dimensional problems are presented. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the memoryless quasi-Newton method, that is precisely the quasi-Newton method for which the approximation to the inverse of Hessian, at each step, is updated from the identity matrix. Hence its search direction can be computed without the storage of matrices. In this paper, a scaled memoryless symmetric rank one (SR1) method for solving large-scale unconstrained optimization problems is developed. The basic idea is to incorporate the SR1 update within the framework of the memoryless quasi-Newton method. However, it is well-known that the SR1 update may not preserve positive definiteness even when updated from a positive definite matrix. Therefore we propose the memoryless SR1 method, which is updated from a positive scaled of the identity, where the scaling factor is derived in such a way that positive definiteness of the updating matrices are preserved and at the same time improves the condition of the scaled memoryless SR1 update. Under very mild conditions it is shown that, for strictly convex objective functions, the method is globally convergent with a linear rate of convergence. Numerical results show that the optimally scaled memoryless SR1 method is very encouraging. [Copyright &y& Elsevier]

We propose a quasi-Newton line-search method that uses negative curvature directions for solving unconstrained optimization problems. In this method, the symmetric rank-one (SR1) rule is used to update the Hessian approximation. The SR1 update rule is known to have a good numerical performance; however, it does not guarantee positive definiteness of the updated matrix. We first discuss the details of the proposed algorithm and then concentrate on its practical behaviour. Our extensive computational study shows the potential of the proposed method from different angles, such as its performance compared with some other existing packages, the profile of its computations, and its large-scale adaptation. We then conclude the paper with the convergence analysis of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses stabilization of an optimization procedure to determine an appropriate semivariogram parameter using the empirical semivariogram for Kriging-based approximation. From a viewpoint of a computational cost for constructing a surrogate model, a semivariogram fitting approach using the empirical semivariogram can be usable for the parameter estimation of a semivariogram function. However, instability of the optimization procedure for determination of the semivariogram parameter may be observed in some cases and it causes to generate an invalid surrogate model. For this problem, a simple technique for stabilization of the optimization for the parameter determination is proposed in this paper. The proposed approach employs a normalization technique of input data with respect to values of variables and an objective function. The proposed method is applied to some numerical examples, and the numerical results illustrate validity and effectiveness of the proposed method. [Copyright &y& Elsevier]

This paper proposes a large-sample approximation of the maximum likelihood (ML) criterion for the joint estimation of nominal directions and angular spreads in the presence of multiple spatially spread sources. The key idea is the concentration on the exact likelihood function by replacing the parametric nuisance estimate, which depends on all unknown parameters at the critical point, by another estimate relying on only the angles of interest, such as nominal angles and angular spreads. Rather than the (3NS +1)-dimensional optimization required by the exact ML estimator, the proposed large-sample approximation allows 2NS-dimensional search, where NS is the number of sources. To demonstrate the proposed estimator, numerical results are conducted for the illustration of estimation error variance. In the non-asymptotic region, the proposed estimator outperforms previous approaches adopting the 2NS-dimensional search. [ABSTRACT FROM AUTHOR]

Abstract: Given the representation theorem, it is well known that any fuzzy set can be represented by an infinite family of its -cuts. While there have been a lot of theoretical investigations along this line, a surprisingly limited attention has been paid to the optimization of the representation (approximation) of fuzzy sets by some finite, usually quite limited, family of their -cuts. In this study, we formulate a problem of the best approximation of a fuzzy set by a finite number of its -cuts. Being concise, the task is formulated as follows: for a given fuzzy set and a prescribed finite number of a-cuts, optimize the values of the corresponding thresholds (a-cuts), so that the obtained finite representation as a nested set of intervals approximates the original fuzzy set to the highest possible extent. While for several (say, 2 or 3) threshold values detailed paper-and-pencil derivations could be accomplished thus leading to the construction of an analytic solution, in general, we need to resort to some optimization procedures. Considering the requirements of the resulting optimization problem formulated with this regard, we use here a certain biologically inspired optimization technique known as particle swarm optimization (PSO). In the paper, we elaborate on some categories of important and commonly encountered problems in which the capabilities of fuzzy sets are fully exploited, including decision-making and data analysis (supported by means of fuzzy clustering). The study includes a series of detailed numeric experiments that illustrate the performance of the PSO and demonstrate the effectiveness of the solutions developed through such optimization. [Copyright &y& Elsevier]

Abstract: Multiagent systems have been studied and widely used in the field of artificial intelligence and computer science to catalyze computation intelligence. In this paper, a multiagent evolutionary algorithm called RAER based on the ERA multiagent modeling pattern is proposed, where ERA has the same architecture as Swarm including three parts of Environment, Reactive rules and Agents. RAER integrates a novel roulette inversion operator (RIO) proposed in this paper and theoretically proved to conquer the irrationality of the inversion operator (IO) designed by John Holland when used for real code stochastic optimization algorithms. Experiments for numerical optimization of 4 benchmark functions show that the RIO operator bears better functioning than IO operator. And experiments for numerical optimization of 12 benchmark functions are used to examine the performance and scalability of RAER along the problem dimensions ranging 20–10000, results indicate that RAER outperforms other comparative algorithms significantly. Also, two engineering optimization problems of a stable linear system approximation and a welded beam design are used to examine the applicability of RAER. Results show that RAER has better search ability and faster convergence speed. Especially for the approximation problem, REAR can find the proper optima belonging to different fixed search areas, which is significantly better than other algorithms and shows that RAER can search the problem domains more thoroughly than other algorithms. Hence, RAER is efficient and practical. [Copyright &y& Elsevier]

In this paper, we study the quadratic model updating problems by using symmetric low-rank correcting, which incorporates the measured model data into the analytical quadratic model to produce an adjusted model that matches the experimental model data, and minimizes the distance between the analytical and updated models. We give a necessary and sufficient condition on the existence of solutions to the symmetric low-rank correcting problems under some mild conditions, and propose two algorithms for finding approximate solutions to the corresponding optimization problems. The good performance of the two algorithms is illustrated by numerical examples. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In recent years there has been a considerable amount of work on the development of numerical methods for derivative-free optimization problems. Some of this work relies on the management of the geometry of sets of sampling points for function evaluation and model building. In this paper we continue the work developed in Math. Program., 111, 141–172) for complete or determined interpolation models (when the number of interpolation points equals the number of basis elements), considering now the cases where the number of points is higher (regression models) and lower (underdetermined models) than the number of basis components. We show that the regression and underdetermined models essentially have similar properties to the interpolation model in that the mechanisms and concepts which control the quality of the sample sets, and hence of the approximation error bounds, of the interpolation models can be extended to the over- and underdetermined cases. We also discuss the trade-offs between using a fully determined interpolation model and the over- or underdetermined ones. [ABSTRACT FROM PUBLISHER]

In this paper, a motion-compensated de-interlacing algorithm using the Markov random field (MRF) model is proposed. The de-interlacing problem is formulated as a maximum a posteriori (MAP) MRF problem. The MAP solution is the one that minimizes an energy function, which imposes discontinuity-adaptive smoothness (DAS) spatial constraint on the de-interlaced frame. The edge direction information, which is used to formulate the DAS constraint, is implicitly indicated by weight vectors (weights for 16 digitized directions). Generally, large weights are assigned to along-edge directions and relatively small weights are assigned to across-edge directions. As a local statistical-based method, the proposed weighting method should be more robust than traditional edge-directed interpolation methods in deciding local edge directions. The proposed algorithm is implemented by an iterative optimization process, which guarantees convergence. However, a global optimal solution is not guaranteed due to computational complexity concern. Simulation results compare the proposed algorithm to other motion compensated de-interlacing algorithms. Significant improvements of de-interlaced edges are observed. [ABSTRACT FROM AUTHOR]

The proper choice of mapping used in space-mapping optimization algorithms is typically problem dependent. The number of parameters of the space-mapping surrogate model must be adjusted so that the model is flexible enough to reflect the features of the fine model, but at the same time is not over flexible. Its extrapolation capability should allow the prediction of the fine model response in the neighborhood of the current iteration point. A wrong choice of space-mapping type may lead to poor performance of the space-mapping optimization algorithm. In this paper, we consider a space-mapping optimization algorithm with an adaptive surrogate model. This allows us to adjust the type of space-mapping surrogate model used in a given iteration based on the approximation/extrapolation capability of the model. The technique does not require any additional fine model evaluations. [ABSTRACT FROM AUTHOR]

This paper proposes a line search technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribière-Polyak conjugate gradient algorithm. It is proved that this line search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the Zoutendijk condition holds under mild assumptions. It is also proved that the resulting conjugate gradient algorithm is convergent under a strong convexity assumption. For the nonconvex case, a globally convergent modification is proposed. Numerical tests are presented. [ABSTRACT FROM AUTHOR]

In this paper, we significantly extend the applicability of state-of-the-art ELDP (equations for linearizing discrete product terms) method by providing a new linearization to handle more complicated non-linear terms involving both of discrete and bounded continuous variables. A general class of “representable programming problems” is formally proposed for a much wider range of engineering applications. Moreover, by exploiting the logarithmic feature embedded in the discrete structure, we present an enhanced linear reformulation model which requires half an order fewer equations than the original ELDP. Computational experiments on various engineering design problems support the superior computational efficiency of the proposed linearization reformulation in solving engineering optimization problems with discrete and bounded continuous variables. [ABSTRACT FROM AUTHOR]

This paper extends the Sequential Unconstrained Minimization Technique for nonlinear programming to include problems where the constraints are a mixture of inequalities and equalities. Theorems indicating the dual nature of the method and the solution of a subproblem are given. Finally, the theoretical basis for a k-point extrapolation procedure is established. [ABSTRACT FROM AUTHOR]

This paper introduces a new disjunctive formulation for the simultaneous optimization and heat integration of systems with variable inlet and outlet temperatures in process streams as well as the possibility of selecting and using different utilities. The starting point is the original compact formulation of the Pinch Location Method, however, instead of approximating the “maximum” operator with smooth, but non-convex functions, these operators are modeled by means of a disjunction. The new formulation has shown to have equal or lower relaxation gap than the best alternative reformulation, thus reducing computational time and numerical problems related to non-convex approximations. [ABSTRACT FROM AUTHOR]

A soft computing approach based on artificial neural network (ANN) and optimization is presented for the numerical solution of the unsteady one-dimensional advection–dispersion equation (ADE) arising in contaminant transport through porous media. A length factor ANN method, based on automatic satisfaction of arbitrary boundary conditions (BCs) was chosen for the numerical solution of ADE. The strength of ANN is exploited to construct a trial approximate solution (TAS) for ADE in a way that it satisfies the initial or BCs exactly. An unsupervised error is constructed in approximating the solution of ADE which is minimized by training ANN using gradient descent algorithm (GDA). Two challenging test problems of ADE are considered in this paper, in which, the first problem has steep boundary layers near x = 1 and many numerical methods create non-physical oscillation near steep boundaries. Also for the second problem many numerical schemes suffer from computational noise and instability issues. The proposed method is advantageous as it does not require temporal discretization for the solution of the ADEs as well as it does not suffer from numerical instability. The reliability and effectiveness of the presented algorithm is investigated by sufficient large number of independent runs and comparison of results with other existing numerical methods. The results show that the present method removes the difficulties arising in the solution of the ADEs and provides solution with good accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a new definition of the filled function is given. Based on the new definition, a new class of filled functions is constructed, and the properties of the new filled functions are analysed and discussed. Moreover, according to the new class of filled functions, a criterion is given to decide whether the point we have obtained is an approximate global optimal solu- tion. Finally, a global optimization algorithm based on the new class of filled functions is presented. The implementation of the algorithm on several test problems is reported with numerical results. [ABSTRACT FROM AUTHOR]

In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely parametrized operators is crucial in order to enhance the online solution of reduced-order models (ROMs). However, in many cases such an affine decomposition is not readily available, and must be recovered through (often) intrusive procedures, such as the empirical interpolation method (EIM) and its discrete variant DEIM. In this paper we show that MDEIM represents a very efficient approach to deal with complex physical and geometrical parametrizations in a non-intrusive, efficient and purely algebraic way. We propose different strategies to combine MDEIM with a state approximation resulting either from a reduced basis greedy approach or Proper Orthogonal Decomposition. A posteriori error estimates accounting for the MDEIM error are also developed in the case of parametrized elliptic and parabolic equations. Finally, the capability of MDEIM to generate accurate and efficient ROMs is demonstrated on the solution of two computationally-intensive classes of problems occurring in engineering contexts, namely PDE-constrained shape optimization and parametrized coupled problems. [ABSTRACT FROM AUTHOR]

A 4D-Var data assimilation technique is applied to a rectangular-box configuration of the NEMO in order to analyze the optimal parametrization of boundary conditions at lateral boundaries. The impact of staircase-shaped coastlines is studied by rotating the model grid around the center of the box. Rotations on 30 and 45 are studied with single and double gyre forcing patterns. It is shown that optimized boundary conditions compensate the errors induced by the staircase-like approximation of the coastline. [ABSTRACT FROM AUTHOR]

A complex matrix P is called Hermitian and {κ +}-potent if Pκ+1 = P = P* for some integer κ ≥ 1. Let P and Q be n x n Hermitian and {κ+1}-potent matrices, we say that complex matrix A is {P,Q,κ+1}-reexive (anti-reexive) if PAQ = A (PAQ = -A). In this paper, the solvability conditions and the general solutions of the left and right inverse eigenvalue problem for {P,Q,κ+1}-reexive and anti-reexive matrices are derived, and the minimal and maximal rank solutions are given. Moreover, the associated optimal approximation problem is also considered. Finally, numerical example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

An improved meshless density variable approximation is incorporated into the BESO method for topology optimization of continuum structures in this paper. The essential boundary condition is enforced by using the compactly supported radial basis function (CSRBF). The Shepard function is used to create a physically meaningful dual-level density approximation. Numerical examples show that the proposed method is feasible and fidelity for the topology optimization of continuum structures. The common numerical instabilities of the BESO method do not exist in the final results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the low rank approximation of the symmetric positive semidefinite matrix, which arises in machine learning, quantum chemistry and inverse problem. We first characterize the feasible set by , and then transform low rank approximation into an unconstrained optimization problem. Finally, we use the nonlinear conjugate gradient method with exact line search to compute the optimal low rank symmetric positive semidefinite approximation of the given matrix. Numerical examples show that the new method is feasible and effective. [Copyright &y& Elsevier]

Abstract: This paper deals with an optimization based method for synthesis of adjustable planar four-bar, crank-rocker mechanisms. For multiple different and desired paths to be traced by a point on the coupler, a two stage method first determines the parameters of the possible driving dyads. Then the remaining mechanism parameters are determined in the second stage where a least-squares based circle-fitting procedure is used. Compared to existing formulations, the optimization method uses less number of design variables. Two numerical examples demonstrate the effectiveness of the proposed synthesis method. [Copyright &y& Elsevier]

Abstract: From numerical point of view, analysis and optimization in computational material engineering require efficient approaches for microstructure representation. This paper develops an approach to establish an image-based interpolation model in order to efficiently parameterize microstructures of a representative volume element (RVE), based on proper orthogonal decomposition (POD) reduction of density maps (snapshots). When the parameters of the RVE snapshot are known a priori, the geometry and topology of individual phases of a parameterized snapshot is given by a series of response surfaces of the projection coefficients in terms of these parameters. Otherwise, a set of pseudo parameters corresponding to the detected dimensionality of the data set are taken from learning the manifolds of the projection coefficients. We showcase the approach and its potential applications by considering a set of two-phase composite snapshots. The choice of the number of retained modes is made after considering both the image reconstruction errors as well as the convergence of the effective material constitutive behavior obtained by numerical homogenization. [Copyright &y& Elsevier]

This paper presents a method for the energy-optimal operation of a fixed-wing aircraft tracking a prescribed landing path in the three-dimensional space with a fixed time of arrival. The problem is converted to an optimal control problem with one state variable, which is subject to state and control input constraints along the path. It is shown that the solution to this energy-optimal tracking problem provides a good approximation to the minimum-fuel problem. The switching structure of the optimal solution is analyzed, and a semi-analytical method is proposed for computing the optimal solution. Compared to standard numerical optimization methods the proposed method is guaranteed to converge to the optimal solution, and it is computationally much more efficient. Numerical examples are presented to demonstrate the validity of the proposed approach. As verified by these numerical results the proposed energy-optimal solution can help improve aircraft fuel efficiency during the landing phase. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we are aimed to solve the non-dissipative Degasperis–Procesi equation based on the formulation. To resolve the computational difficulty at the wave crest where the first-order derivative may diverge and the shockpeakon solution may form, the first-order spatial derivative term in the two-step equations will be approximated in a conservative form. The resulting equations will be approximated by the symplecticity-preserving time-stepping scheme and the spatial discretization scheme that can optimize the numerical wavenumber for the first-order spatial derivative term. This scheme will be developed in a three-point grid stencil with the accuracy order of seventh within the combined compact finite difference framework. Besides the validation of numerical accuracy, we will in particular address the discrete conservation of Hamiltonians even when peakon collides with antipeakon and generates, as a result, a shockpeakon. We will also demonstrate the capability of applying the proposed numerical method to sharply resolve some important features of the third-order dispersive DP equation. [Copyright &y& Elsevier]

Abstract: In this paper, the solution of fuzzy linear system (FLS) is investigated based on a -level expansion. To this end, -level of FLS is solved for calculating the core of fuzzy solution and then its spreads are obtained by solving an optimization problem with a special objective function. Using our proposed method, if the computed solution satisfies the FLS, it can be as exact or approximated solution. Finally, the existence of solution of FLS is proved in details and some numerical examples are solved to illustrate the accuracy and capability of the method. [Copyright &y& Elsevier]