Papers in this group
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The local convergence properties of a class of primal-dual interior point methods are analyzed. These methods are designed to minimize a nonlinear, nonconvex, objective function subject to linear equality constraints and general inequalities. They…
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In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these…
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Infeasible-interior-point paths for sufficient linear complementarity problems and their analyticityIn this paper we study the behavior of infeasible-interior-point-paths for solving horizontal linear complementarity problems that are sufficient in the sense of Cottle et al. (R.W. Cottle, J.-S. Pang, Venkateswaran, Linear Algebra Appl. 114/115…
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The limits of a class of primal and dual solution trajectories associated with the Sequential Unconstrained Minimization Technique (SUMT) are investigated for convex programming problems with non-unique optima. Logarithmic barrier terms are assumed.…
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We consider nonlinear programs with inequality constraints, and we focus on the problem of identifying those constraints which will be active at an isolated local solution. The cor- rect identification of active constraints is important from both a…
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We introduce a new framework for the convergence analysis of a class of distributed constrained non-convex optimization algorithms in multi-agent systems. The aim is to search for local minimizers of a non-convex objective function which is supposed…
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We consider column sufficient linear complementarity problems and study the prob- lem of identifying those variables that are zero at a solution. To this end we propose a new, computa- tionally inexpensive technique that is based on growth…
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We examine the sequence of local minimizers of the log-barrier function for a nonlinear pro- gram near a solution at which second-order sufficient conditions and the Mangasarian-Fromovitz constraint qualification are satisfied, but the active…
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A technique for the resolution of degeneracy in an Active Set Method for Quadratic Programming is described. The approach generalises Fletcher's method [2] which applies to the LP case. The method is described in terms of an LCP tableau, which is…
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The objectives of this paper are twofold. We devise a general framework for identify- ing locally optimal algorithmic parameters. Algorithmic parameters are treated as decision variables in a problem for which no derivative knowledge or existence is…
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We introduce a framework in which updating rules for the barrier parame- ter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the…
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The asymptotic convergence of parameterized variants of Newton’s method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to…
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Aninterior-point method for nonlinear programming is presented. It enjoys the flexibility of switch- ing between a line search method that computes steps by factoring the primal-dual equations and a trust region method that uses a conjugate gradient…
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Special methods for dealing with constraints of the formxj= xk, called variable upper bounds, were introduced by Schrage. Here we describe a method that circumvents the massive degeneracy inherent in these constraints and show how it can be…
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We introduce the OPAL framework in which the identification of good algorithmic parameters is interpreted as a black box optimization problem whose variables are the algorithmic parameters. In addition to the target algorithm, the user of the…
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A new primal-dual algorithm is proposed for the minimization of non-convex objective functions subject to general inequality and linear equality constraints. Themethod uses a primal-dual trust-region model to ensure descent on a suitable merit…
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