On NCP-FunctionsComputational Optimization and Applications - Tập 13 - Trang 201-220 - 1999
Defeng Sun, Liqun Qi
In this paper we reformulate several NCP-functions for the nonlinear complementarity problem (NCP) from their merit function forms and study some important properties of these NCP-functions. We point out that some of these NCP-functions have all the nice properties investigated by Chen, Chen and Kanzow [2] for a modified Fischer-Burmeister function, while some other NCP-functions may lose one or s...... hiện toàn bộ
A Heuristic for Moment-Matching Scenario GenerationComputational Optimization and Applications - Tập 24 - Trang 169-185 - 2003
Kjetil Høyland, Michal Kaut, Stein W. Wallace
In stochastic programming models we always face the problem of how to represent the random variables. This is particularly difficult with multidimensional distributions. We present an algorithm that produces a discrete joint distribution consistent with specified values of the first four marginal moments and correlations. The joint distribution is constructed by decomposing the multivariate proble...... hiện toàn bộ
Using approximate secant equations in limited memory methods for multilevel unconstrained optimizationComputational Optimization and Applications - Tập 51 - Trang 967-979 - 2011
Serge Gratton, Vincent Malmedy, Philippe L. Toint
The properties of multilevel optimization problems defined on a hierarchy of discretization grids can be used to define approximate secant equations, which describe the second-order behavior of the objective function. Following earlier work by Gratton and Toint (2009) we introduce a quasi-Newton method (with a linesearch) and a nonlinear conjugate gradient method that both take advantage of this n...... hiện toàn bộ
TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalitiesComputational Optimization and Applications - - 2010
Benedetta Morini, Margherita Porcelli
The Matlab implementation of a trust-region Gauss-Newton method for bound-constrained nonlinear least-squares problems is presented. The solver, called TRESNEI, is adequate for zero and small-residual problems and handles the solution of nonlinear systems of equalities and inequalities. The structure and the usage of the solver are described and an extensive numerical comparison with functions fro...... hiện toàn bộ
Two methods for the maximization of homogeneous polynomials over the simplexComputational Optimization and Applications - Tập 80 - Trang 523-548 - 2021
Faizan Ahmed, Georg Still
The paper deals with the numerical solution of the problem P to maximize a homogeneous polynomial over the unit simplex. We discuss the convergence properties of the so-called replicator dynamics for solving P. We further examine an ascent method, which also makes use of the replicator transformation. Numerical experiments with polynomials of different degrees illustrate the theoretical convergenc...... hiện toàn bộ
Second order semi-smooth Proximal Newton methods in Hilbert spacesComputational Optimization and Applications - Tập 82 - Trang 465-498 - 2022
Bastian Pötzl, Anton Schiela, Patrick Jaap
We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering differentiability and convexity than in existing theory. As far as differentiability of the smooth part of the objective function is concerned, we introduce the notion of ...... hiện toàn bộ
An alternating direction and projection algorithm for structure-enforced matrix factorizationComputational Optimization and Applications - Tập 68 - Trang 333-362 - 2017
Lijun Xu, Bo Yu, Yin Zhang
Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning techniques useful in many applications including neuroscience and signal processing. In this paper, we present a unified algorithm framework, based on the classic alternating directio...... hiện toàn bộ
A computational analysis of lower bounds for big bucket production planning problemsComputational Optimization and Applications - Tập 53 - Trang 729-753 - 2012
Kerem Akartunalı, Andrew J. Miller
In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As wi...... hiện toàn bộ