First- and Second-Order Optimality Conditions for Quadratically Constrained Quadratic Programming Problems

We consider a quadratic programming problem with quadratic cone constraints and an additional geometric constraint. Under suitable assumptions, we establish necessary and sufficient conditions for optimality of a KKT point and, in particular, we characterize optimality by using strong duality as a r...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2022-06, Vol.193 (1-3), p.118-138
Main Authors: Flores-Bazán, Fabián, Mastroeni, Giandomenico
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Engineering
Geometric constraints
Hessian matrices
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic equations
Quadratic programming
Theory of Computation
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Summary:We consider a quadratic programming problem with quadratic cone constraints and an additional geometric constraint. Under suitable assumptions, we establish necessary and sufficient conditions for optimality of a KKT point and, in particular, we characterize optimality by using strong duality as a regularity condition. We consider in details the case where the feasible set is defined by two quadratic equality constraints and, finally, we analyse simultaneous diagonalizable quadratic problems, where the Hessian matrices of the involved quadratic functions are all diagonalizable by means of the same orthonormal matrix.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02022-1