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A New Sequential Optimality Condition for Constrained Nonsmooth Optimization

Elias S. Helou(elias***at***icmc.usp.br)
Sandra A. Santos(sandra***at***ime.unicamp.br)
Lucas E. A. Simões(simoes.lea***at***gmail.com)

Abstract: We introduce a sequential optimality condition for locally Lipschitz constrained nonsmooth optimization, verifiable just using derivative information, and which holds even in the absence of any constraint qualification. The proposed sequential optimality condition is not only novel for nonsmooth problems, but brings new insights for the smooth case as well. We present a practical algorithm that generates iterates fulfilling the new necessary optimality condition. A main feature of the devised algorithm is to allow a stronger control over the infeasibility of the iterates than usually obtained by exact penalty strategies, ensuring theoretical and practical advantages. Illustrative numerical experiments highlight the potentialities of the algorithm.

Keywords: nonsmooth nonconvex optimization; constrained optimization; sequential optimality condition; constraint qualification

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 11/23/2018
Entry Accepted: 11/23/2018
Entry Last Modified: 11/23/2018

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