Abstract
Conic linear programs in locally convex Hausdorff topological vector spaces are addressed in this paper. Solution existence for the dual problem, as well as solution existence for the primal problem, and strong duality, are proved under minimal regularity assumptions. Namely, to get the results and a Farkas-type theorem for infinite-dimensional conic linear inequalities, we employ the generalized Slater condition either for the primal problem or for the dual problem, as well as proper separation and the concept of quasi-regularity of convex sets. Illustrative examples are presented.
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Acknowledgements
This research is funded by the Vietnam Ministry of Education and Training under grant number B2022-CTT-06. The authors are indebted to an anonymous expert for very useful comments on an earlier version of the paper, which have helped us to improve the presentation and get some refinements of the previous results. We would like to thank the handling Associate Editor and the referee for their careful readings and useful suggestions.
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Communicated by Nguyen Mau Nam.
Dedicated to Professor Boris S. Mordukhovich on the occasion of his 75th birthday.
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Luan, N.N., Yen, N.D. Strong Duality and Solution Existence Under Minimal Assumptions in Conic Linear Programming. J Optim Theory Appl (2023). https://doi.org/10.1007/s10957-023-02318-w
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DOI: https://doi.org/10.1007/s10957-023-02318-w
Keywords
- Infinite-dimensional conic linear program
- Dual pair
- Compatible topology in the dual space
- Strong duality
- Solution existence
- Generalized Slater condition
- Quasi-regularity of convex sets