generalized hessian – Optimization Online

Estimates of generalized Hessians for optimal value functions in mathematical programming

Published: 2017/10/19

Convex and Nonsmooth Optimization coderivative, generalized hessian, optimal value function, parametric optimization, second order subdifferential, sensitivity analysis

The \emph{optimal value function} is one of the basic objects in the field of mathematical optimization, as it allows the evaluation of the variations in the \emph{cost/revenue} generated while \emph{minimizing/maximizing} a given function under some constraints. In the context of stability/sensitivity analysis, a large number of publications have been dedicated to the study of continuity … Read more

Partial Smoothness,Tilt Stability, and Generalized Hessians

Published: 2011/10/17

Adrian Lewis

Shanshan Zhang

Nonsmooth Optimization generalized hessian, nonsmooth optimization, partial smoothness, prox-regular, second-order, sensitivity analysis, subdifferential continuity, tilt stability, variational analysis

We compare two recent variational-analytic approaches to second-order conditions and sensitivity analysis for nonsmooth optimization. We describe a broad setting where computing the generalized Hessian of Mordukhovich is easy. In this setting, the idea of tilt stability introduced by Poliquin and Rockafellar is equivalent to a classical smooth second-order condition. ArticleDownload View PDF