Given a convex program with $C^2$ functions and a convex set $S$ of solutions to the problem, we give a second order condition which guarantees that the problem does not have solutions outside of $S$. This condition is interpreted as a characterization for the quadratic growth of the cost function. The crucial role in the proofs is played by a theorem describing a certain uniform regularity property of critical cones in smooth convex programs. We apply these results to the discussion of stability of solutions of a convex program under possibly nonconvex perturbations.
Publié le : 1994-07-05
Classification:
MULTIPLE SOLUTIONS,
CRITICAL CONE,
QUADRATIC GROWTH,
STABILITY,
CONVEXITY,
LAGRANGIAN,
COMPOSITE FUNCTIONS,
[INFO.INFO-OH]Computer Science [cs]/Other [cs.OH],
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{Report N°: RR-2403,
author = {Bonnans, J. Frederic and Ioffe, Alexander D.},
title = {Quadratic growth and stability in convex programming problems},
journal = {HAL},
volume = {1994},
number = {0},
year = {1994},
language = {en},
url = {http://dml.mathdoc.fr/item/Report N°: RR-2403}
}
Bonnans, J. Frederic; Ioffe, Alexander D. Quadratic growth and stability in convex programming problems. HAL, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/Report%20N%C2%B0:%20RR-2403/