A modified goal programming approach for the mean-absolute deviation portfolio optimization model

The purpose of this paper is to present a reformulation of the model presented by Feinstein and Thapa [C.D. Feinstein, M.N. Thapa, Notes: a reformulation of a mean-absolute deviation portfolio optimization model, Management Science 39 (12) (1993) 1552-1553]. The approach of Feinstein and Thapa has been accepted as the most efficient technique published, requiring the least number of auxiliary constraints and additional continuous variables. To solve a portfolio optimization problem with T periods, in their method would introduce T + 2 auxiliary constraints, 2T auxiliary sign constraints, and 2T additional continuous variables. This note indicates that it is still possible to reduce the number of auxiliary constraints and additional continuous variables in the model of Feinstein and Thapa. The equivalent concise model is proposed in this note, which has T + 2 auxiliary constraints, T auxiliary sign constraints, and T additional continuous variables.