# Quadratic growth and stability in convex programming problems

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.
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https://hal.inria.fr/inria-00074272
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• HAL Id : inria-00074272, version 1

### Citation

J. Frederic Bonnans, Alexander D. Ioffe. Quadratic growth and stability in convex programming problems. [Research Report] RR-2403, INRIA. 1994. ⟨inria-00074272⟩

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