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Minimization of the maximum function of a special form. (Russian) Zbl 0736.90070

This paper is concerned with the problem of minimizing the maximum function \(F\) of a special form, i.e. \[ F(x)=\max_{1\leq i\leq m}f_ i(x_ i), \] where \(f_ i:\;D_ i\subset R^{n_ i}\to R\) are continuous functions on convex closed sets \(D_ i\) for \(i=1,\dots,m\). By \(D\) we denote the set \(D=\{x(x_ 1,\dots,x_ m)\in R^ n:\) \(x_ i\in D_ i\), \(i=1,\dots,m\}\), \(n=\sum^ n_{i=1}n_ i\).
In this work the author proposes a method for solving the constrained optimization problem \(\min_{x\in D}F(x)\). This kind of problem arises in practice particularly in projecting complex technical systems. The proposed method takes into account the special form of the objective function and allows the possibility of parallel minimization processes, i.e. the solution of the problems \(\min_{x_ i\in D_ i}f_ i(x_ i)\) is sufficient for solving the original problem.

MSC:

90C30 Nonlinear programming
49K35 Optimality conditions for minimax problems
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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