Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the 2nd kind

2014/04/18 by Juan-Carlos De Los Reyes, Christian Meyer, Reyes, Juan-Carlos De Los +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1404.4787

openalex publication_date 2014/04/18 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the solution map is studied. Directional differentiability is proved both for finite-dimensional and function space problems, under suitable assumptions on the active set. A characterization of B- and strong stationary optimal solutions is obtained thereafter. Finally, based on the obtained first-order information, a trust-region algorithm is proposed for the solution of the optimization problems.

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