Search

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]

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]

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]

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]

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]

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 proposes a new approximation scheme which is an extension to the well-established Charef s approximation method for fractional order systems. The method relaxes the constraints on the locations of the pole-zero pairs of the approximate system, which provides more flexibility and space for approximate system to approach the original system as close as possible. The approxi-mate system based on an optimization process performs not only a good magnitude fitting but also a good phase fitting. The benefits from using the proposed scheme are illustrated by numerical examples in frequency domains. [ABSTRACT FROM AUTHOR]

Abstract: Recently, graph-based spectral clustering algorithms have been developing rapidly, which are proposed as discrete combinatorial optimization problems and approximately solved by relaxing them into tractable eigenvalue decomposition problems. In this paper, we first review the current existing spectral clustering algorithms in a unified-framework way and give a straightforward explanation about spectral clustering. We also present a novel model for generalizing the unsupervised spectral clustering to semi-supervised spectral clustering. Under this model, prior information given by some instance-level constraints can be generalized to space-level constraints. We find that (undirected) graph built on the enlarged prior information is more meaningful, hence the boundaries of the clusters are more correct. Experimental results based on toy data, real-world data and image segmentation demonstrate the advantages of the proposed model. [Copyright &y& Elsevier]

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]

Abstract: Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new symmetric rank-one (SR1) method for the solution of unconstrained optimization problems. The proposed method involves an algorithm in which the usual SR1 Hessian is updated a number of times in a way to be specified in some iterations, to improve the performance of the Hessian approximation. In particular, we discuss how to consider a criterion for indicating at each iteration whether it is necessary to employ extra updates. However it is well known that there are some theoretical difficulties when applying the SR1 update. Even for a current positive definite Hessian approximation, it is possible that the SR1 update may not be defined or the SR1 update may not preserve positive definiteness at some iterations. We then employ a restarting procedure that guarantees that updated matrices will be well-defined while preserving positive definiteness of updates. Numerical results support these theoretical considerations. They show that the implementation of the SR1 method using extra updating techniques improves the performance of the SR1 method substantially for a number of test problems from the literature. [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: In this paper, by solving the relaxed quasiconcave programming problem in outcome space, a new global optimization algorithm for convex multiplicative programming is presented. Two kinds of techniques are employed to establish the algorithm. The first one is outer approximation technique which is applied to shrink relaxation area of quasiconcave programming problem and to compute appropriate feasible points and to raise the capacity of bounding. And the other one is branch and bound technique which is used to guarantee global optimization. Some numerical results are presented to demonstrate the effectiveness and feasibility of the proposed algorithm. [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]

Abstract: In this paper we consider a conic trust-region method for unconstrained optimization problems and analyze its convergence properties. We propose a convenient curvilinear search method to approximately solve the arising conic trust-region subproblem. Note that this approximate method preserves the strong convergence properties of the exact solution methods and is easy to implement. Both the linear and superlinear convergence of the method are established under commonly used conditions. Numerical experiments are conducted to show the efficiency of the new method. [Copyright &y& Elsevier]

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]