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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Vydáno v:Journal of optimization theory and applications Ročník 193; číslo 1-3; s. 118 - 138
Hlavní autoři: Flores-Bazán, Fabián, Mastroeni, Giandomenico
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.06.2022
Springer Nature B.V
Témata:
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
90C20
Duality
Quadratic optimization
90C46
Karush–Kuhn–Tucker conditions
ISSN:0022-3239, 1573-2878
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02022-1