second order regularity – Optimization Online

Differentiability properties of metric projections onto convex sets

Published: 2013/11/14, Updated: 2014/08/17

Convex and Nonsmooth Optimization cone reducibility, directional differentiability, metric projection, nondegeneracy, second order regularity

It is known that directional differentiability of metric projection onto a closed convex set in a finite dimensional space is not guaranteed. In this paper we discuss sufficient conditions ensuring directional differentiability of such metric projections. The approach is based on a general theory of sensitivity analysis of parameterized optimization problems. Article Download View Differentiability … Read more

Sensitivity analysis of parameterized variational inequalities

Published: 2003/06/16

Alexander Shapiro

Complementarity and Variational Inequalities gap functions, locally upper lipschitz and h, second order growth condition, second order regularity, sensitivity analysis, variational inequality

We discuss in this paper continuity and differentiability properties of solutions of parameterized variational inequalities (generalized equations). To this end we use an approach of formulating variational inequalities in a form of optimization problems and applying a general theory of perturbation analysis of parameterized optimization problems. Citation School of Industrial and Systems Engineering, Georgia Institute … Read more