Nonmonotone algorithm for minimax optimization problems. (English) Zbl 1215.65114

The paper deals with finite minimax optimization problems \[ \min_{x\in\mathbb{R}^n}\;\max_{1\leq i\leq m}\, f_i(x), \] where all functions \(f_i\) are twice continuously differentiable. Equivalently, the function \(\Phi(x)= \max f_i(x)\) is to minimize. The problem is not necessarily differentiable, but it is possible to transform the task to a differentiable programming problem with side conditions (inequalities). The authors introduce a nonmonotone algorithm for the construction of a minimizing sequence. The algorithm takes not only the advantage of nonmonotone strategy and second-order step but also the advantages of trust-region methods and line search methods. The new algorithm is of strongly global convergence and superlinear convergence. Numerical experiments (10 examples) indicate the efficiency.


65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C47 Minimax problems in mathematical programming
Full Text: DOI


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