Second Order Optimality Conditions Based on Parabolic Second Order Tangent Sets
- 1 January 1999
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 9 (2) , 466-492
- https://doi.org/10.1137/s1052623496306760
Abstract
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.Keywords
This publication has 34 references indexed in Scilit:
- Robust solutions of uncertain linear programsOperations Research Letters, 1999
- Optimization Problems with Perturbations: A Guided TourSIAM Review, 1998
- Conjugate Duality in Set-Valued Vector OptimizationJournal of Mathematical Analysis and Applications, 1997
- On Eigenvalue OptimizationSIAM Journal on Optimization, 1995
- Perturbation analysis of optimization problems in banach spacesNumerical Functional Analysis and Optimization, 1992
- Variational analysis of a composite function: A formula for the lower second order epi-derivativeJournal of Mathematical Analysis and Applications, 1991
- On pseudo-differentiabilityTransactions of the American Mathematical Society, 1991
- First- and second-order epi-differentiability in nonlinear programmingTransactions of the American Mathematical Society, 1988
- A unified theory of first and second order conditions for extremum problems in topological vector spacesPublished by Springer Nature ,1982
- Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear SystemsSIAM Journal on Numerical Analysis, 1976