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Characterizations of solution sets of cone-constrained convex programming problems

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Abstract

In this paper, we consider a type of cone-constrained convex program in finite-dimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an optimal solution. Moreover, some necessary conditions and sufficient conditions are established which simplifies the corresponding results in Jeyakumar et al. (J Optim Theory Appl 123(1), 83–103, 2004). In particular, when the cone reduces to three specific cones, that is, the \(p\)-order cone, \(L^p\) cone and circular cone, we show that the obtained results can be achieved by easier ways by exploiting the special structure of those three cones.

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Acknowledgments

The authors are very grateful to the referees for their constructive comments, which have considerably improved the paper.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, People’s Republic of China

    Xin-He Miao

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Jein-Shan Chen

Authors
  1. Xin-He Miao
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  2. Jein-Shan Chen
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Correspondence to Jein-Shan Chen.

Additional information

The author’s work is supported by Ministry of Science and Technology, Taiwan.

X.-H. Miao is supported by National Young Natural Science Foundation (No. 11101302) and National Natural Science Foundation of China (No. 11471241).

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Miao, XH., Chen, JS. Characterizations of solution sets of cone-constrained convex programming problems. Optim Lett 9, 1433–1445 (2015). https://doi.org/10.1007/s11590-015-0900-9

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  • DOI: https://doi.org/10.1007/s11590-015-0900-9

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