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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]

The constrained convex minimization problem is to find a point xn with the property that xn ϵ C, and h(xn ) = min h(x), ∀x ϵ C, where C is a nonempty, closed, and convex subset of a real Hilbert space H, h(x) is a real-valued convex function, and h(x) is not Fréchet differentiable, but lower semicontinuous. In this paper, we discuss an iterative algorithm which is different from traditional gradient-projection algorithms. We firstly construct a bifunction F1 (x, y) defined as F1 (x, y) = h(y) - h(x). And we ensure the equilibrium problem for F1 (x, y) equivalent to the above optimization problem. Then we use iterative methods for equilibrium problems to study the above optimization problem. Based on Jung's method (2011), we propose a general approximation method and prove the strong convergence of our algorithm to a solution of the above optimization problem. In addition, we apply the proposed iterative algorithm for finding a solution of the split feasibility problem and establish the strong convergence theorem. The results of this paper extend and improve some existing results [ABSTRACT FROM AUTHOR]

Most real-world engineering optimization problems are inherently multi objective, for example, searching for trade-off solutions of high quality and low cost. As no single optimal solution exists for such problems, multi objective optimizers provide sets of optimal (or near-optimal) trade-off solutions to choose from. The empirical attainment function (EAF) is a powerful tool that can be used to analyze and compare the performance of these optimizers. While the visualization of EAFs is rather straightforward in two objectives, the three-objective case presents a great challenge as we need to visualize a large number of 3D cuboids. This paper addresses the visualization of exact as well as approximated 3D EAF values and differences in these values provided by two competing multi objective optimizers. We show that the exact EAFs can be visualized using slicing and maximum intensity projection (MIP), while the approximated EAFs can be visualized using slicing, MIP, and direct volume rendering. In addition, the paper demonstrates the use of the proposed visualization techniques on a steel casting optimization problem. [ABSTRACT FROM AUTHOR]

The research on the triangle packing problem has important theoretic significance, which has broad application prospects in material processing, network resource optimization, and so forth. Generally speaking, the orientation of the triangle should be limited in advance, since the triangle packing problem is NP-hard and has continuous properties. For example, the polygon is not allowed to rotate; then, the approximate solution can be obtained by optimization method. This paper studies the triangle packing problem by a new kind of method. Such concepts as angle region, corner-occupying action, corner-occupying strategy, and edge-conjoining strategy are presented in this paper. In addition, an edge-conjoining and corner-occupying algorithm is designed, which is to obtain an approximate solution. It is demonstrated that the proposed algorithm is highly efficient, and by the time complexity analysis and the analogue experiment result is found. [ABSTRACT FROM AUTHOR]

The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized-sparse- approximate-inverse- (FSAI-) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI-IC preconditioner, which combines the FSAI and the Block Jacobi-IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallel hypre package, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI-Fortran 90 language and exhibits good scalability up to one thousand processors. [ABSTRACT FROM AUTHOR]

One-parameter families of Newton's iterative method for the solution of nonlinear equations and its extension to unconstrained optimization problems are presented in the paper. These methods are derived by implementing approximations through a straight line and through a parabolic curve in the vicinity of the root. The presented variants are found to yield better performance than Newton's method, in addition that they overcome its limitations. [ABSTRACT FROM AUTHOR]

Adaptive Dynamic Programming (ADP) with critic-actor architecture is an effective way to perform online learning control. To avoid the subjectivity in the design of a neural network that serves as a critic network, kernel-based adaptive critic design (ACD) was developed recently. There are two essential issues for a static kernel-based model: how to determine proper hyperparameters in advance and how to select right samples to describe the value function. They all rely on the assessment of sample values. Based on the theoretical analysis, this paper presents a two-phase simultaneous learning method for a Gaussian-kernel-based critic network. It is able to estimate the values of samples without infinitively revisiting them. And the hyperparameters of the kernel model are optimized simultaneously. Based on the estimated sample values, the sample set can be refined by adding alternatives or deleting redundances. Combining this critic design with actor network, we present a Gaussian-kernel-based Adaptive Dynamic Programming (GK-ADP) approach. Simulations are used to verify its feasibility, particularly the necessity of two-phase learning, the convergence characteristics, and the improvement of the system performance by using a varying sample set. [ABSTRACT FROM AUTHOR]

This paper presents an Improved Genetic Algorithm with Two-Level Approximation (IGATA) to minimize truss weight by simultaneously optimizing size, shape, and topology variables. On the basis of a previously presented truss sizing/topology optimization method based on two-level approximation and genetic algorithm (GA), a new method for adding shape variables is presented, in which the nodal positions are corresponding to a set of coordinate lists. A uniform optimization model including size/shape/topology variables is established. First, a first-level approximate problem is constructed to transform the original implicit problem to an explicit problem. To solve this explicit problem which involves size/shape/topology variables, GA is used to optimize individuals which include discrete topology variables and shape variables. When calculating the fitness value of each member in the current generation, a second-level approximation method is used to optimize the continuous size variables. With the introduction of shape variables, the original optimization algorithm was improved in individual coding strategy as well as GA execution techniques. Meanwhile, the update strategy of the first-level approximation problem was also improved. The results of numerical examples show that the proposed method is effective in dealing with the three kinds of design variables simultaneously, and the required computational cost for structural analysis is quite small. [ABSTRACT FROM AUTHOR]

More recently, with the increasing demand of web services on the World Wide Web used in the Internet of Things (IoTs), there has been a growing interest in the study of efficient web service quality evaluation approaches based on prediction strategies to obtain accurate quality-of-service (QoS) values. However, it is obvious that the web service quality changes significantly under the unpredictable network environment. Such changes impose very challenging obstacles to web service QoS prediction. Most of the traditional web service QoS prediction approaches are implemented only using a set of static model parameters with the help of designer’s a priori knowledge. Unlike the traditional QoS prediction approaches, our algorithm in this paper is realized by incorporating approximate dynamic programming- (ADP-) based online parameter tuning strategy into the QoS prediction approach. Through online learning and optimization, the proposed approach provides the QoS prediction with automatic parameter tuning capability, and prior knowledge or identification of the prediction model is not required. Therefore, the near-optimal performance of QoS prediction can be achieved. Experimental studies are carried out to demonstrate the effectiveness of the proposed ADP-based prediction approach. [ABSTRACT FROM AUTHOR]

For the case of the single snapshot, the integrated SNR gain could not be obtained without the multiple snapshots, which degrades the mutual coupling correction performance under the lower SNR case. In this paper, a Convex Chain MUSIC (CC-MUSIC) algorithm is proposed for the mutual coupling correction of the L-shaped nonuniform array with single snapshot. It is an online self-calibration algorithm and does not require the prior knowledge of the correction matrix initialization and the calibration source with the known position. An optimization for the approximation between the no mutual coupling covariance matrix without the interpolated transformation and the covariance matrix with the mutual coupling and the interpolated transformation is derived. A global optimization problem is formed for the mutual coupling correction and the spatial spectrum estimation. Furthermore, the nonconvex optimization problem of this global optimization is transformed as a chain of the convex optimization, which is basically an alternating optimization routine. The simulation results demonstrate the effectiveness of the proposed method, which improve the resolution ability and the estimation accuracy of the multisources with the single snapshot. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of L2-L∞ model reduction for continuous-time nonlinear uncertain systems. The approach of the construction of a reduced-order model is presented for high-order nonlinear uncertain systems described by the T-S fuzzy systems, which not only approximates the original high-order system well with an L2-L∞ error performance level γ but also translates it into a linear lower-dimensional system. Then, the model approximation is converted into a convex optimization problem by using a linearization procedure. Finally, a numerical example is presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes an alternative mesh less approach to solve partial differential equations (PDEs). With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm(EA) is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE) is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced. [ABSTRACT FROM AUTHOR]

We construct a neural network based on smoothing approximation techniques and projected gradient method to solve a kind of sparse reconstruction problems. Neural network can be implemented by circuits and can be seen as an importantmethod for solving optimization problems, especially large scale problems. Smoothing approximation is an efficient technique for solving nonsmooth optimization problems. We combine these two techniques to overcome the difficulties of the choices of the step size in discrete algorithms and the item in the set-valued map of differential inclusion. In theory, the proposed network can converge to the optimal solution set of the given problem. Furthermore, some numerical experiments show the effectiveness of the proposed network in this paper. [ABSTRACT FROM AUTHOR]

Derivatives of eigenvectors with respect to structural parameters play an important role in structural design, identification, and optimization. Particularly, calculation of eigenvector sensitivity is considered when the eigenvalues are repeated. A relaxation factor embedded in the combined approximations (CA) method makes it effective to the structural response at various modified designs. The proposed method is feasible after overcoming the defection of irreversibility of the characteristic matrix. Numerical examples show that it is easy to implement the computational procedure, and the method presented in this paper is efficient for the general linear vibration damped systems with repeated frequencies. [ABSTRACT FROM AUTHOR]

The scan chain insertion problem is one of the mandatory logic insertion design tasks. The scanning of designs is a very efficient way of improving their testability. But it does impact size and performance, depending on the stitching ordering of the scan chain. In this paper, we propose a graph-based approach to a stitching algorithm for automatic and optimal scan chain insertion at the RTL. Our method is divided into two main steps. The first one builds graph models for inferring logical proximity information from the design, and then the second one uses classic approximation algorithms for the traveling salesman problem to determine the best scan-stitching ordering. We show how this algorithm allows the decrease of the cost of both scan analysis and implementation, by measuring total wirelength on placed and routed benchmark designs, both academic and industrial. [ABSTRACT FROM AUTHOR]

We discuss the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity. The approaches are presented to compute positive approximation and interpolation by solving the two corresponding optimization problems. Numerical experiments are provided to illustrate that the proposed method is flexible. [ABSTRACT FROM AUTHOR]

We develop a sufficient descent method for solving large-scale unconstrained optimization problems. At each iteration, the search direction is a linear combination of the gradient at the current and the previous steps. An attractive property of this method is that the generated directions are always descent. Under some appropriate conditions, we show that the proposed method converges globally. Numerical experiments on some unconstrained minimization problems from CUTEr library are reported, which illustrate that the proposed method is promising. [ABSTRACT FROM AUTHOR]

The article presents the study conducted regarding the use of multiobjective optimization tool in dealing free structure analog circuit design. This novel approach is using genetic algorithms and incorporating parasitics for a free structure circuit. The scheme has conducted because the sensitivity calculations of the circuit as polynomial approximation for design is not accessible. This sensitivity to component variations is addressed through the tool and incorporated in the fitness evaluation operation.

We apply an analytical method called the Optimal Parametric Iteration Method (OPIM) to multispecies Lotka-Volterra equations. By using initial values, accurate explicit analytic solutions have been derived. The method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement has been demonstrated between the obtained solutions and the numerical ones. This new approach, which can be easily applied to other strongly nonlinear problems, is very effective and yields very accurate results. [ABSTRACT FROM AUTHOR]

Fixed-basis and variable-basis approximation schemes are compared for the problems of function approximation and functional optimization (also known as infinite programming). Classes of problems are investigated for which variable-basis schemes with sigmoidal computational units perform better than fixed-basis ones, in terms of the minimum number of computational units needed to achieve a desired error in function approximation or approximate optimization. Previously known bounds on the accuracy are extended, with better rates, to families of d-variable functions whose actual dependence is on a subset of d' ≪ d variables, where the indices of these d' variables are not known a priori. [ABSTRACT FROM AUTHOR]

The concepts of α-well-posedness, αwell-posedness in the generalized sense, L-α-well-posedness and L-α-well-posedness in the generalized sense for mixed quasi variational-like inequality problems are investigated. We present some metric characterizations for these well-posednesses. [ABSTRACT FROM AUTHOR]

We apply mollifiers to study the properties of real functions which satisfy mean value conditions and present new equivalent conditions for complex analytic functions. New properties of complex functions with mean value conditions are given. [ABSTRACT FROM AUTHOR]

A hybrid method combining the FR conjugate gradient method and the WYL conjugate gradient method is proposed for unconstrained optimization problems. The presented method possesses the sufficient descent property under the strong Wolfe-Powell (SWP) line search rule relaxing the parameter σ < 1. Under the suitable conditions, the global convergence with the SWP line search rule and the weak Wolfe-Powell (WWP) line search rule is established for nonconvex function. Numerical results show that this method is better than the FR method and the WYL method. [ABSTRACT FROM AUTHOR]

In the present work, we consider a class of nonlinear optimal control problems, which can be called "optimal control problems in mechanics." We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm. [ABSTRACT FROM AUTHOR]