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Smooth optimization methods in discrete minimax problems. (English) Zbl 0708.90083
Rep. Moscow Refusnik Semin., Ann. N. Y. Acad. Sci. 491, 191-193 (1987).
[For the entire collection see Zbl 0705.00008.]
The author states that under continuous differentiability of the functions involved and boundedness of certain sets, an optimal solution of a minimax problem exists and Kuhn-Tucker conditions are satisfied. Under certain strict regularity conditions and the assumption of twice differentiability, a new Lagrangian is introduced. This Lagrangian is shown to have some useful properties that the Kuhn-Tucker Lagrangian does not seem to possess. These properties help construct a general method to solve the original problem. The convergence rate of a generated sequence is specified under the assumption that the procedure has a geometric or superlinear or quadratic rate of convergence.

MSC:
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49J35 Existence of solutions for minimax problems
90-08 Computational methods for problems pertaining to operations research and mathematical programming