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Dual method for solving a special problem of quadratic programming as a subproblem at nonlinear minimax approximation. (English) Zbl 0621.65061
This paper concerns the nonlinear minimax approximation problem, where a point \(x^*\in R^ n\) is sought such that \(F(x^*)=\min_{x\in R^ n}(\max_{i\in M}f_ i(x))\) where \(f_ i(x)\), \(i\in M\) are real-valued functions defined in the n-dimensional vector space \(R^ n\), with continuous second-order derivatives, and \(M=\{1,...,m\}\). To solve this problem the method of recursive quadratic programming is applied where the most important step is the solution of a special quadratic programming subproblem. In this paper a dual method is presented in detail for solving this quadratic programming problem and its finite step convergence is proved.
Reviewer: T.Rapcsák

MSC:
65K05 Numerical mathematical programming methods
90C20 Quadratic programming
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References:
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