4,289 research outputs found
Experiences with reduction method to solve semi-infinite programming problems
In this talk, some variants of reduction-type method combined with a line search filter
method to solve nonlinear semi-infinite programming problems are presented. We use the
stretched simulated annealing method and the branch and bound technique to compute
the maximizers of the constraint. The filter method is used as an alternative to merit
functions to promote convergence from poor starting points
A smoothing projected Newton-type algorithm for semi-infinite programming
2008-2009 > Academic research: refereed > Publication in refereed journa
Deflation for semismooth equations
Variational inequalities can in general support distinct solutions. In this
paper we study an algorithm for computing distinct solutions of a variational
inequality, without varying the initial guess supplied to the solver. The
central idea is the combination of a semismooth Newton method with a deflation
operator that eliminates known solutions from consideration. Given one root of
a semismooth residual, deflation constructs a new problem for which a
semismooth Newton method will not converge to the known root, even from the
same initial guess. This enables the discovery of other roots. We prove the
effectiveness of the deflation technique under the same assumptions that
guarantee locally superlinear convergence of a semismooth Newton method. We
demonstrate its utility on various finite- and infinite-dimensional examples
drawn from constrained optimization, game theory, economics and solid
mechanics.Comment: 24 pages, 3 figure
Comparative study of RPSALG algorithm for convex semi-infinite programming
The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.This research was partially supported by MINECO of Spain, Grants MTM2011-29064-C03-01/02
A New Exact Penalty Function Method for Continuous Inequality Constrained Optimization Problems
publisher-authenticated version online. Alternate Location: Permanent Link: The attached document may provide the author's accepted version of a published work. See Citation for details of the published work
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