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Outer approximation scheme for weakly convex constrained optimization problems
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DOI：10.1007/s10898-026-01609-6.png)
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Abstract
En 中文
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.
Keywords:
Weak convexity
QCQP
Outer approximation
Quadratic cuts
Cutting sphere algorithm
Journal
J
IF:
1.7
Papers:
80
Citations:
6.9K