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Conic Linear Programming Duals for Classes of Quadratic Semi-Infinite Programs with Applications

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Abstract

In this paper, we first present strong conic linear programming duals for convex quadratic semi-infinite problems with linear constraints and geometric index sets. The obtained results show that the optimal values of a convex quadratic semi-infinite problem with convex compact sets and its associated conic linear programming dual problem are equal with the solution attainment of the dual program. We then prove that the conic linear programming dual is equivalently reformulated as a second-order cone programming problem whenever the index sets are ellipsoids, balls, cross-polytopes or boxes. As an application, we show that a class of separable fractional quadratic semi-infinite programs also admits second-order cone programming duality under ellipsoidal index sets.

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Acknowledgements

This research was supported by The VNUHCM-University of Information Technology’s Scientific Research Support Fund. The authors would like to thank the editor and reviewer for valuable comments and suggestions. The second author is grateful to Professor V. Jeyakumar for discussing the topic when he was working at the University of New South Wales, Sydney.

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Authors and Affiliations

  1. Vietnam National University, Ho Chi Minh City, Vietnam

    Cao Thanh Tinh

  2. Department of Mathematics and Physics, University of Information Technology, Ho Chi Minh City, Vietnam

    Cao Thanh Tinh

  3. Department of Mathematics and Applications, Saigon University, 273 An Duong Vuong Street, District 5, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

  4. School of Engineering, RMIT University, Melbourne, VIC, 3000, Australia

    Thai Doan Chuong

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  1. Cao Thanh Tinh
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  2. Thai Doan Chuong
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Correspondence to Thai Doan Chuong.

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Communicated by Marco Antonio López-Cerdá

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Tinh, C.T., Chuong, T.D. Conic Linear Programming Duals for Classes of Quadratic Semi-Infinite Programs with Applications. J Optim Theory Appl 194, 570–596 (2022). https://doi.org/10.1007/s10957-022-02040-z

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