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Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming

Priscila S. Ferreira (pri.savulski***at***hotmail.com)
Elizabeth W. Karas (ewkaras***at***gmail.com)
Mael Sachine (mael***at***ufpr.br)
Francisco Sobral (chicosobral***at***gmail.com)

Abstract: In this work we present an algorithm for solving constrained optimization problems that does not make explicit use of the objective function derivatives. The algorithm mixes an inexact restoration framework with filter techniques, where the forbidden regions can be given by the flat or slanting filter rule. Each iteration is decomposed in two independent phases: a feasibility phase which reduces an infeasibility measure without evaluations of the objective function, and an optimality phase which reduces the objective function value. As the derivatives of the objective function are not available, the optimality step is computed by derivative-free trust-region internal iterations. Any technique to construct the trust-region models can be used since the gradient of the model is a reasonable approximation of the gradient of the objective function at the current point. Assuming this and classical assumptions, we prove that the full steps are efficient in the sense that near a feasible nonstationary point, the decrease in the objective function is relatively large, ensuring the global convergence results of the algorithm. Numerical experiments show the effectiveness of the proposed method.

Keywords: Nonlinear programming, derivative-free optimization, inexact restoration, filter methods, global convergence, numerical experiments

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Technical Report, Federal University of Paraná, Brazil, July, 2015. Update in August, 2016.

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Entry Submitted: 07/22/2015
Entry Accepted: 07/22/2015
Entry Last Modified: 08/31/2016

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