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Primal interior point method for minimization of generalized minimax functions. (English) Zbl 1204.49022
Summary: We propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning its implementation covering numerical differentiation, variable metric updates, and a barrier parameter decrease. Using standard weak assumptions, we prove that this algorithm is globally convergent if a bounded barrier is used. Then, using stronger assumptions, we prove that it is globally convergent also for the logarithmic barrier. Finally, we present results of computational experiments confirming the efficiency of the primal interior point method for special cases of generalized minimax problems.

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