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 always holds in the case of semi-definite programming.
Publié le : 1996-07-05
Classification:
SEMI-INFINITE PROGRAMMING,
DUALITY,
TANGENT SETS,
LAGRANGE MULTIPLIERS,
CONE CONSTRAINTS,
SECOND ORDER OPTIMALITY CONDITIONS,
SEMI-DEFINITE PROGRAMMING,
[INFO.INFO-OH]Computer Science [cs]/Other [cs.OH],
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{Report N°: RR-2952,
author = {Bonnans, J. Frederic and Cominetti, Roberto and Shapiro, Alexander},
title = {Second Order Necessary and Sufficient Optimality Conditions under Abstract Constraints},
journal = {HAL},
volume = {1996},
number = {0},
year = {1996},
language = {en},
url = {http://dml.mathdoc.fr/item/Report N°: RR-2952}
}
Bonnans, J. Frederic; Cominetti, Roberto; Shapiro, Alexander. Second Order Necessary and Sufficient Optimality Conditions under Abstract Constraints. HAL, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/Report%20N%C2%B0:%20RR-2952/