Exact Dual Bounds for Some Nonconvex Minimax Quadratic Optimization Problems

Abstract

The nonconvex separable minimax quadratic optimization problem is analyzed. Two approaches to the problem solution are described, namely, by using SOCP relaxation and by using Lagrangian relaxation of a quadratic extremum analog problem. A condition is obtained that guarantees finding the value and the global extremum point of the problem of the considered class by calculating the dual bound of the equivalent quadratic extremum problem.

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Correspondence to O. A. Berezovskyi.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2021, pp. 115–122.

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Berezovskyi, O.A. Exact Dual Bounds for Some Nonconvex Minimax Quadratic Optimization Problems. Cybern Syst Anal 57, 101–107 (2021). https://doi.org/10.1007/s10559-021-00333-1

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Keywords

  • minimax quadratic optimization problem
  • SOCP relaxation
  • Lagrangian relaxation
  • exact dual bound
  • positive definite matrix