computational experiments – Page 2

Interior-point method for nonlinear programming with complementarity constraints

Published: 2009/02/25

Constrained Nonlinear Optimization, Nonlinear Optimization complementarity constraints, computational experiments, indefinite preconditioners, indefinite systems, interior point methods, merit functions, nonlinear programming, preconditioned conjugate gradient

In this report, we propose an algorithm for solving nonlinear programming problems with com-plementarity constraints, which is based on the interior-point approach. Main theoretical results concern direction determination and step-length selection. We use an exact penalty function to remove complementarity constraints. Thus a new indefinite linear system is defined with a tridiagonal low-right submatrix. Inexact … Read more

Primal interior point method for minimization of generalized minimax functions

Published: 2008/01/12

Ladislav Lukšan

Ctirad Matonoha

Jan Vlček

Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization computational experiments, generalized minimax optimization, global convergence, interior point methods, large-scale optimization, modified newton methods, nonsmooth optimization, unconstrained optimization, variable metric methods

In this report, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning … Read more

A shifted Steihaug-Toint method for computing a trust-region step.

Published: 2004/09/17

Ladislav Lukšan

Ctirad Matonoha

Jan Vlček

Unconstrained Optimization computational experiments, conjugate gradient method, krylov subspaces, large-scale optimization, trust-region methods, unconstrained optimization

Trust-region methods are very convenient in connection with the Newton method for unconstrained optimization. The More-Sorensen direct method and the Steihaug-Toint iterative method are most commonly used for solving trust-region subproblems. We propose a method which combines both of these approaches. Using the small-size Lanczos matrix, we apply the More-Sorensen method to a small-size trust-region … Read more