A geometric characterization of strong duality in nonconvex quadratic programming with linear and nonconvex quadratic constraints

We first establish a relaxed version of Dines theorem associated to quadratic minimization problems with finitely many linear equality and a single (nonconvex) quadratic inequality constraints. The case of unbounded optimal valued is also discussed. Then, we characterize geometrically the strong dua...

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Bibliographic Details
Published in:Mathematical programming 2014-06, Vol.145 (1-2), p.263-290
Main Authors: Flores-Bazán, Fabián, Cárcamo, Gabriel
Format: Article
Language:English
Subjects:
Analysis
Asymptotic properties
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Full Length Paper
Inequalities
Inequality
Lagrange multiplier
Mathematical and Computational Physics
Mathematical functions
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Minimization
Numerical Analysis
Optimization
Quadratic programming
Studies
Theorems
Theoretical
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Summary:We first establish a relaxed version of Dines theorem associated to quadratic minimization problems with finitely many linear equality and a single (nonconvex) quadratic inequality constraints. The case of unbounded optimal valued is also discussed. Then, we characterize geometrically the strong duality, and some relationships with the conditions employed in Finsler theorem are established. Furthermore, necessary and sufficient optimality conditions with or without the Slater assumption are derived. Our results can be used to situations where none of the results appearing elsewhere are applicable. In addition, a revisited theorem due to Frank and Wolfe along with that due to Eaves is established for asymptotically linear sets.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0647-y