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Minimax balayage theorem and an inscribed ball problem. (English. Russian original) Zbl 0568.49007
Math. Notes 30, 542-548 (1982); translation from Mat. Zametki 30, 109-121 (1981).
A balayage theorem is a result which makes it possible in a certain sense to shrink (”balayer”) the region of optimization of a given functional without changing the optimal value. Such results go back to a well-known theorem of de la Vallée-Poussin and have been studied by numerous workers.
The goals of this paper are the following: 1) to focus attention on the dual nature of balayage, which shows up in a number of important cases; 2) to carry over balayage theorems to cover certain nonconvex problems; 3) to consider the ”inscribed” ball problem as an example.
MSC:
49J35 Existence of solutions for minimax problems
49J45 Methods involving semicontinuity and convergence; relaxation
49N15 Duality theory (optimization)
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
49J50 Fréchet and Gateaux differentiability in optimization
90C25 Convex programming
90C30 Nonlinear programming
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References:
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