Computational schemes for large-scale problems in extended linear- quadratic programming (Q1813335)

The aim of this paper is to present a specific class of methods solving an extended linear-quadratic programming problem. A new class of algorithms, called finite-envelope methods, is described. These methods, which exploit duality very strongly, reduce the task of solving a problem of high dimensionality to that of solving a sequence of low-dimensional ordinary quadratic programming subproblems. Finite-envelope methods in some special cases of two-stage stochastic programming had been introduced by the author and \textit{R. J.-B. Wets} [Math. Program. Study 28, 63-93 (1986; Zbl 0559.90090); and in: Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 545-560 (1986; Zbl 0661.90065)].