Quadratic Programming

Convex quadratic programming as applied to portfolio planning is established and well understood. In this paper, presented in two parts, we highlight the importance of choosing an algorithm that processes a family of problems efficiently. In Part I (published in issue 8/3), in particular, we described an adaptation of the simplex method for Quadratic Programming (QP). The method not only takes advantage of the sparse features of simplex, the use of the duality property makes it ideally suited for processing the discrete optimization models. Part II of the paper considers a family of discrete QP formulations of the portfolio problem, which capture threshold constraints and cardinality restrictions. We describe the adaptation a novel method branch, fix and relax to process this class of models efficiently. Theory and computational results are presented.

Convex quadratic programming (QP) as applied to portfolio planning is established and well understood. In this paper, presented in two parts, we highlight the importance of choosing an algorithm that processes a family of problems efficiently. In Part I in particular we describe an adaptation of the simplex method for QP. The method takes advantage of the sparse features of simplex and the use of the duality property makes it ideally suited for processing the discrete optimization models. Part II (to be published in issue 8/4) of the paper considers a family of discrete QP formulations of the portfolio problem, which captures threshold constraints and cardinality restrictions. We describe the adaptation of a novel method branch, fix and relax to process this class of models efficiently. Theory and computational results are presented.