Strong duality and KKT conditions in nonconvex optimization with a single equality constraint and geometric constraint

Strong duality and KKT conditions in nonconvex optimization with a single equality constraint and... Some topological and geometric characterizations of strong duality for a non convex optimization problem under a single equality and geometric constraints are established. In particular, a hidden convexity of the conic hull of joint-range of the pair of functions associated to the original problem, is obtained. Applications to derive (a characterization of the validity of) KKT conditions without standard constraints qualification, are also discussed. It goes beyond the exact penalization technique. Several examples showing our results provide much more information than those appearing elsewhere, are given. Finally, the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Programming Springer Journals

Strong duality and KKT conditions in nonconvex optimization with a single equality constraint and geometric constraint

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
ISSN
0025-5610
eISSN
1436-4646
D.O.I.
10.1007/s10107-016-1078-3
Publisher site
See Article on Publisher Site

Abstract

Some topological and geometric characterizations of strong duality for a non convex optimization problem under a single equality and geometric constraints are established. In particular, a hidden convexity of the conic hull of joint-range of the pair of functions associated to the original problem, is obtained. Applications to derive (a characterization of the validity of) KKT conditions without standard constraints qualification, are also discussed. It goes beyond the exact penalization technique. Several examples showing our results provide much more information than those appearing elsewhere, are given. Finally, the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail.

Journal

Mathematical ProgrammingSpringer Journals

Published: Oct 15, 2016

References

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