An improved partial bundle method for linearly constrained minimax problems

  • Chunming Tang Guangxi University
  • Huangyue Chen Guangxi University
  • Jinbao Jian Yulin Normal University
Keywords: Minimax problems, Bundle method, Partial cutting-planes model, Global convergence, Subgradient aggregation

Abstract

In this paper, we propose an improved partial bundle method for solving linearly constrained minimax problems. In order to reduce the number of component function evaluations, we utilize a partial cutting-planes model to substitute for the traditional one. At each iteration, only one quadratic programming subproblem needs to be solved to obtain a new trial point. An improved descent test criterion is introduced to simplify the algorithm. The method produces a sequence of feasible trial points, and ensures that the objective function is monotonically decreasing on the sequence of stability centers. Global convergence of the algorithm is established. Moreover, we utilize the subgradient aggregation strategy to control the size of the bundle and therefore overcome the difficulty of computation and storage. Finally, some preliminary numerical results show that the proposed method is effective.

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Published
2016-02-28
How to Cite
Tang, C., Chen, H., & Jian, J. (2016). An improved partial bundle method for linearly constrained minimax problems. Statistics, Optimization & Information Computing, 4(1), 84-98. https://doi.org/10.19139/soic.v4i1.205
Section
Research Articles