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Approximate-KKT stopping criterion when Lagrange multipliers are not available

Gabriel Haeser(gabriel.haeser***at***unifesp.br)
Vinícius V. de Melo(vinicius.melo***at***unifesp.br)

Abstract: In this paper we investigate how to efficiently apply Approximate-Karush-Kuhn-Tucker (AKKT) proximity measures as stopping criteria for optimization algorithms that do not generate approximations to Lagrange multipliers, in particular, Genetic Algorithms. We prove that for a wide range of constrained optimization problems the KKT error measurement tends to zero. We also develop a simple model to compute the KKT error measure requiring only the solution of a non-negative linear least squares problem. Our numerical experiments show the efficiency of the strategy.

Keywords: Optimality Conditions, Genetic Algorithms, Stopping Criteria

Category 1: Nonlinear Optimization

Citation:

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Entry Submitted: 01/21/2013
Entry Accepted: 01/21/2013
Entry Last Modified: 01/21/2013

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