Assessing the potential of interior point barrier filter line search methods: nonmonotoneversusmonotone approach

Abstract

In this article, we present a numerical study of three nonmonotone filter line search techniques, as well as a three-dimensional filter approach, when incorporated into the solver IPOPT, a primal-dual barrier method developed by Wa¨chter and Biegler [On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program. 106 (2006), pp. 25-57] for nonlinear programming. Primary assessment of the proposals has been done with sets of small-and medium-scale problems and large-scale problems separately. Results show that the use of nonmonotone globalization strategies improves efficiency.

Multilocal Programming: A Derivative-Free Filter Multistart Algorithm

“…The filter methodology appears naturally from the observation that an optimal solution of the problem (1) minimizes both constraint violation and objective function [3,4,7,9]. Thus, the proposed CS method is combined with a (line search) filter method that aims at generating trial iterates that might be acceptable if they improve the constraint violation or the objective function relative to the current iterate.…”

A Derivative-Free Filter Driven Multistart Technique for Global Optimization

“…To measure progress towards an optimal solution a filter methodology, as outlined in [4], is integrated into the local search procedure. The filter methodology appears naturally from the observation that an optimal solution of the problem (1) minimizes both constraint violation and objective function [2,3,5,4].…”

“…Hence, the progress towards a solution that is feasible and optimal is carried out by a filter method. This is a recent strategy that has shown to be highly competitive with penalty function methods [2][3][4]. This paper is organized as follows.…”

Nonmonotone hybrid tabu search for inequalities and equalities: an experimental study

“…, p are twice continuously differentiable. Thus, methods for solving the least squares problem cannot be directly applied to solve (3). Besides, when a global solution is required, classical local search methods, like Newton-type methods, have some disadvantages, compared with global search methods.…”

“…Under mild conditions, global convergence has been guaranteed. These nonmonotone strategies have been applied in different contexts, for example, coupled with Quasi-Newton methods for systems of equations in [8], for solving complementarity problems [18], integrated into primal-dual interior point and barrier methods [2,3] and in a Newton-type method when solving a smooth reformulation of the system (1) [45]. In this paper, we aim at studying the behavior of a nonmonotone combined hybrid TS method when computing a solution of the system (1) by converging to a global minimizer of the merit function (3).…”