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<p>We introduce a novel outer approximation scheme specifically designed for solving weakly convex constrained optimization problems. The key idea lies in utilizing quadratic cuts, rather than the traditional linear cuts, and solving an outer approximation problem at each iteration in the form of a Quadratically Constrained Quadratic Programming (QCQP) problem. The primary result demonstrated in this work is that every convergent subsequence generated by the proposed outer approximation scheme converges to a global minimizer of the general weakly convex optimization problem under consideration. To enhance the practical implementation of this method, we also propose two variants of the algorithm. The approach is illustrated through its application to the Multiclass Neyman-Pearson classification problem.</p>

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Outer approximation scheme for weakly convex constrained optimization problems

  • 期刊论文

  • 发表日期：

    2026年4月4日

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  • Ewa M. Bednarczuk,
  • Giovanni Bruccola,
  • Jean-Christophe Pesquet,
  • Krzysztof Rutkowski

摘要

We introduce a novel outer approximation scheme specifically designed for solving weakly convex constrained optimization problems. The key idea lies in utilizing quadratic cuts, rather than the traditional linear cuts, and solving an outer approximation problem at each iteration in the form of a Quadratically Constrained Quadratic Programming (QCQP) problem. The primary result demonstrated in this work is that every convergent subsequence generated by the proposed outer approximation scheme converges to a global minimizer of the general weakly convex optimization problem under consideration. To enhance the practical implementation of this method, we also propose two variants of the algorithm. The approach is illustrated through its application to the Multiclass Neyman-Pearson classification problem.