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1 PROMATH - Mathematical Programming Inria Paris-Rocquencourt

Abstract : 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.

Keywords : MULTIPLE SOLUTIONS CRITICAL CONE QUADRATIC GROWTH STABILITY CONVEXITY LAGRANGIAN COMPOSITE FUNCTIONS





Autor: J. Frederic Bonnans - Alexander D. Ioffe

Fuente: https://hal.archives-ouvertes.fr/



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