The primal algorithm using conjugate directions for quadratic programming problems with simple upper bounds

Abstract

An algorithm that solves quadratic programming problems with a convex objective function and a feasible region defined by constraints Ax=b, β ≦ x ≦ α is presented. The algorithm uses the SUB method [3] to establish a starting feasible point and to construct the starting basis matrix. A feasible direction for the kiteration is chosen from a set of row-vectors of the inverse of the current basis matrix. After a finite number of iterations an optimal solution is found. A conjugacy property of feasible directions, convergence of the algorithm, the question of cycling and a comparison with other algorithms from the same class of methods of feasible directions are discussed.

AMS 1980 Subject Classifications:

• Primary: 65 K 05
• Secondary: 90 C 20
• Secondary: 90 C 25

Keywords:

• Quadratic programming
• feasible directions
• conjugate directions
• the sub algorithm