The major focus of this work is to compare several methods for computing the proximal point of a nonconvex function via numerical testing. To do this, we introduce two techniques for randomly generating challenging nonconvex test functions, as well as two very specific test functions which should be of future interest to Nonconvex Optimization Benchmarking. … Read more
Our goal in this paper is to demonstrate that branch-and-bound algorithms for combinatorial optimization can be effectively implemented on a relatively new type of multiprocessor platform known as a computational grid. We will argue that to easily and effectively harness the power of computational grids for branch-and-bound algorithms, the master-worker paradigm should be used to … Read more
This papers describes a perl language program to create time-to-target solution value plots for measured CPU times that are assumed to fit a shifted exponential distribution. This is often the case in local search based heuristics for combinatorial optimization, such as simulated annealing, genetic algorithms, iterated local search, tabu search, WalkSAT, and GRASP. Such plots … Read more
The present article summarizes the state of the art algorithms to compute the discrete Moreau envelope, and presents a new linear-time algorithm, named NEP for NonExpansive Proximal mapping. Numerical comparisons between the NEP and two existing algorithms: The Linear-time Legendre Transform (LLT) and the Parabolic Envelope (PE) algorithms are performed. Worst-case time complexity, convergence results, … Read more
Computational results obtained when solving a subset of NETLIB problems by using a dense projected gradient implementation of the non-simplex active-set sagitta method presented in [12] are summarized. Two different addition rules for its initial phase are considered and, for each problem solved, two corresponding graphs are reported to illustrate the variations of the objective … Read more
This paper is concerned with the optimization of continuum structures under dynamic loading using methods from topology design. The constraint functions are non-linear and implicit, their evaluation requires the resolution of a computation-intensive finite-element analysis performed by a black-box commercial structural mechanics software such as MSC/Nastran. We first present a brief overview of topology optimization … Read more
We present a simple, scaleable, distributed simplex implementation for large linear programs. It is designed for coarse grained computation, particularly, readily available networks of workstations. Scalability is achieved by using the standard form of the simplex rather than the revised method. Virtually all serious implementations are based on the revised method because it is much … Read more
This paper describes Knitro 5.0, a C-package for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving large-scale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, … Read more
Recent developments in integer-programming software systems have tremendously improved our ability to solve large-scale instances. We review the major algorithmic components of state-of-the-art solvers and discuss the options available to users to adjust the behavior of these solvers when default settings do not achieve the desired performance level. Furthermore, we highlight advances towards integrated modeling … Read more
SparesPOP is a MATLAB implementation of a sparse semidefinite programming (SDP) relaxation method proposed for polynomial optimization problems (POPs) in the recent paper by Waki et al. The sparse SDP relaxation is based on a hierarchy of LMI relaxations of increasing dimensions by Lasserre, and exploits a sparsity structure of polynomials in POPs. The efficiency … Read more