Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs

Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming problems in Banach spaces are established in this paper. Since the decomposition procedures using orthogonality relations in Euclidean spaces and the comp...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 192; no. 2; pp. 426 - 442
Main Author: An, Duong Thi Viet
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2022
Springer Nature B.V
Subjects:
Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Orthogonality
Quadratic programming
Theory of Computation
90C20
generalized quadratic programming problem
generalized polyhedral convex set
second-order optimality condition
90C30
90C46
locally unique solution
90C48
Banach space
49K27
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming problems in Banach spaces are established in this paper. Since the decomposition procedures using orthogonality relations in Euclidean spaces and the compactness of finite-dimensional unit spheres, which worked well for finite-dimensional quadratic programs, cannot be applied to the Banach space setting, a series of new constructions and arguments are proposed. These results give a comprehensive extension of the corresponding theorems on finite-dimensional quadratic programs.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01967-z