Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Mathematics of Operations Research
Mathematics of Operations Research
Second-Order Necessary Optimality Conditions for Problems Without A Priori Normality Assumptions
Mathematics of Operations Research
Generalized semi-infinite programming: A tutorial
Journal of Computational and Applied Mathematics
Local Duality of Nonlinear Semidefinite Programming
Mathematics of Operations Research
Second order sufficient optimality conditions in vector optimization
Journal of Global Optimization
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In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order sufficient conditions. We show that the second order regularity condition always holds in the case of semidefinite programming.