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

Nadav Hallak () and Marc Teboulle ()
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Nadav Hallak: Tel-Aviv University
Marc Teboulle: Tel-Aviv University

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 2, No 7, 480-503

Abstract: 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.

Keywords: Feasible direction methods; Second-order methods; Constrained optimization; Second-order necessary optimality conditions; 90C26; 90C30; 65K05; 90C46; 90C31 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01713-x

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