Dual method for solving a special problem of quadratic programming as a subproblem at linearly constrained nonlinear minimax approximation

In (1.1), f,(x), i e Mj are real-valued functions defined in the n-dimensional vector space Rn with continuous second-order derivatives and Mt u M 2 — {1, ..., m}, M, n M2 = 0. Recently the problem (1.1) has been attracting a considerable attention. To solve this problem, several approaches have been developed, especially the product form of variable metric methods with generalized reduced gradients [4], the methods of recursive linear programming [6] and the methods of recursive quadratic programming [3]. The methods of recursive quadratic programming for solving the problems of minimax approximation were developed in analogy with their original application in the field of nonlinear programming, where we seek a pair (x*, z*)eNn + l such that z* = min z