second-order subdifferentials – Optimization Online

Partial Second-Order Subdifferentials in Variational Analysis and Optimization

Published: 2012/12/26

Nonsmooth Optimization coderivatives, generalized differentiation, parametric constrained optimization, second-order subdifferentials, stability, stationary point mappings, variational analysis

This paper presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and constrained optimization in finite-dimensional spaces. The main results concern developing extended calculus rules for these second-order constructions in both finite-dimensional and infinite-dimensional frameworks. We also provide new applications of partial … Read more

CHARACTERIZATIONS OF FULL STABILITY IN CONSTRAINED OPTIMIZATION

Published: 2012/08/09

Boris S. Mordukhovich

Tyrrell Rockafellar

Ebrahim Sarabi

Nonsmooth Optimization, Robust Optimization constrained parametric optimization, full stability of local minimizers, nonlinear and extended nonlinear programming, parametric prox- regularity and amenability, second-order subdifferentials, strong regularity, variational analysis

This paper is mainly devoted to the study of the so-called full Lipschitzian stability of local solutions to finite-dimensional parameterized problems of constrained optimization, which has been well recognized as a very important property from both viewpoints of optimization theory and its applications. Based on second- order generalized differential tools of variational analysis, we obtain … Read more