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Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs

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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.

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Acknowledgements

This research was supported by the Simons Foundation Grant Targeted for Institute of Mathematics, Vietnam Academy of Science and Technology. The author would like to thank Professor Nguyen Dong Yen for useful comments and suggestions. The careful readings and insightful comments of the two anonymous referees are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Thai Nguyen University of Sciences, Thai Nguyen city, Vietnam

    Duong Thi Viet An

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Duong Thi Viet An

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  1. Duong Thi Viet An
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Correspondence to Duong Thi Viet An.

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Communicated by Nguyen Mau Nam.

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An, D.T.V. Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs. J Optim Theory Appl 192, 426–442 (2022). https://doi.org/10.1007/s10957-021-01967-z

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