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Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

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  • Nadav Hallak

    (Tel-Aviv University
    Ecole Polytechnique Federale de Lausanne)

  • Marc Teboulle

    (Tel-Aviv University)

Abstract

This paper introduces a method for computing points satisfying the second-order necessary optimality conditions for nonconvex minimization problems subject to a closed and convex constraint set. The method comprises two independent steps corresponding to the first- and second-order conditions. The first-order step is a generic closed map algorithm, which can be chosen from a variety of first-order algorithms, making it adjustable to the given problem. The second-order step can be viewed as a second-order feasible direction step for nonconvex minimization subject to a convex set. We prove that any limit point of the resulting scheme satisfies the second-order necessary optimality condition, and establish the scheme’s convergence rate and complexity, under standard and mild assumptions. Numerical tests illustrate the proposed scheme.

Suggested Citation

  • Nadav Hallak & Marc Teboulle, 2020. "Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 480-503, August.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:2:d:10.1007_s10957-020-01713-x
    DOI: 10.1007/s10957-020-01713-x
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    References listed on IDEAS

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