cone reducibility – Optimization Online

A minimal face constant rank constraint qualification for reducible conic programming

Published: 2023/04/26

Cone Programming, Linear, Cone and Semidefinite Programming, Nonlinear Optimization cone reducibility, conic programming, constraint qualifications, facial reduction, second-order necessary optimality conditions

\(\) In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ramírez, T. P. Silveira. First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition. Mathematical Programming, 2023. DOI: 10.1007/s10107-023-01942-8] we introduced a constant rank constraint qualification for nonlinear semidefinite and second-order cone programming by considering all … Read more

Differentiability properties of metric projections onto convex sets

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

Alexander Shapiro

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