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The paper is devoted to the optimization problems with equality constraints in the case when the Lagrange multiplier associated with the objective function might be equal to zero. We introduce a new modified Lagrange system that has a singular solution of the original optimization problem as its regular solution. We obtain conditions under which this solution is a regular locally unique solution of the modified Lagrange system. Our results are based on constructions of the p-regularity theory and the structure of the p-factor.

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Singular Optimization Problems and p-Factor Approach for Their Analysis

  • 会议论文

  • 发表日期：

    2025年

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  • Olga Brezhneva,
  • Yuri Evtushenko,
  • Vlasta Malkova,
  • Alexey Tret’yakov

摘要

The paper is devoted to the optimization problems with equality constraints in the case when the Lagrange multiplier associated with the objective function might be equal to zero. We introduce a new modified Lagrange system that has a singular solution of the original optimization problem as its regular solution. We obtain conditions under which this solution is a regular locally unique solution of the modified Lagrange system. Our results are based on constructions of the p-regularity theory and the structure of the p-factor.