The SUBQ method in quadratic programming
Treść / Zawartość
Author's summary: "In linear programming the simple upper bound method (SUB in short) is well known. It is a modification of the simplex method which finds a minimum of the target function on an admissible set with some additional conditions of the form β≤x≤α imposed on x. "In this paper we present a method which solves the problem of minimization of a quadratic, convex target function on an admissible set defined by conditions of the form β≤x≤α. It is a modification of the C. E. Lemke algorithm [Management Sci. 8 (1961/62), 442–453; MR0148483] for problems of quadratic programming. Because of the special form of the conditions defining the admissible set this method is in a sense a counterpart of the SUB method in linear programming. Therefore we call the algorithm the SUBQ algorithm (the simple upper bound algorithm for quadratic programming). "In Section 2 we give a description of the method based mainly on a geometric interpretation. In Section 3 we present the algorithm and in Section 4 we give a proof of the convergence of the method.''