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On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems

Author

Listed:
  • Xiangkai Sun

    (Chongqing Technology and Business University)

  • Jiayi Huang

    (Chongqing Technology and Business University)

  • Kok Lay Teo

    (Sunway University)

Abstract

In this paper, we deal with a new class of SOS-convex (sum of squares convex) polynomial optimization problems with spectrahedral uncertainty data in both the objective and constraints. By using robust optimization and a weighted-sum scalarization methodology, we first present the relationship between robust solutions of this uncertain SOS-convex polynomial optimization problem and that of its corresponding scalar optimization problem. Then, by using a normal cone constraint qualification condition, we establish necessary and sufficient optimality conditions for robust weakly efficient solutions of this uncertain SOS-convex polynomial optimization problem based on scaled diagonally dominant sums of squares conditions and linear matrix inequalities. Moreover, we introduce a semidefinite programming relaxation problem of its weighted-sum scalar optimization problem, and show that robust weakly efficient solutions of the uncertain SOS-convex polynomial optimization problem can be found by solving the corresponding semidefinite programming relaxation problem.

Suggested Citation

  • Xiangkai Sun & Jiayi Huang & Kok Lay Teo, 2024. "On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems," Journal of Global Optimization, Springer, vol. 88(3), pages 755-776, March.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:3:d:10.1007_s10898-023-01353-1
    DOI: 10.1007/s10898-023-01353-1
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