Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs

Duong Thi Viet An ()
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Duong Thi Viet An: Thai Nguyen University of Sciences

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 2, No 2, 426-442

Abstract: Abstract 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.

Keywords: Banach space; generalized polyhedral convex set; generalized quadratic programming problem; second-order optimality condition; locally unique solution.; 49K27; 90C20; 90C30; 90C46; 90C48 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01967-z

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