Primal interior-point method for large sparse minimax optimization. (English) Zbl 1198.90394

The paper introduces a feasible primal interior point method for solving the problem: minimize \(F(x):=\max_{1\leq i\leq m}f_{i}(x)\), where \(f_{i}:\mathbb{R}^{m}\rightarrow \mathbb{R}\) are functions which are bounded below, and have bounded continuous first and second-order derivatives on the convex hull of a level set of \(F\). It is shown that the algorithm converges globally. In the last section of the paper, the method is compared to three other known methods by testing each one on a set of 22 problems.


90C51 Interior-point methods
90C47 Minimax problems in mathematical programming
90C06 Large-scale problems in mathematical programming
49K35 Optimality conditions for minimax problems


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