Quadratic Programs and Complementarity

Abstract

The optimality criteria associated with a convex minimising quadratic program are shown to form a special type of linear complementarity problem, one that has a symmetric matrix. The dual quadratic programs of Dorn are derived, as are the symmetric dual programs of Cottle which are especially useful in elasto-plastic structural analysis. Cottle’s duality theorem is stated, and attention is given to the joint solution and to the question of uniqueness of solution. Wolfe’s algorithm for solving quadratic programs is discussed. The Wolfe-Markowitz algorithm for solving a parametric quadratic program is introduced, and its use in solving the parametric linear complementarity problem associated with elasto-plastic structural analysis is described.