This paper presents a new primal dual simplex method and investigates the duality formation implying in classical simplex methods. We reviews classical simplex methods for linear programming problems and give a detail discussion for the relation between modern and classical algorithms. The two modified versions are present. The advantages of the new algorithms are simplicity … Read more
In this survey we review the many faces of the S-lemma, a result about the correctness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry and linear algebra as well. These were active research areas, but as … Read more
Managing shelf space is critical for retailers to attract customers and to optimize profit. This paper develops a shelf space allocation optimization model that explicitly incorporates essential in-store costs and considers space- and cross-elasticities. The resultant model maximizes a signomial objective function over linear and bilinear constraints in mixed-integer variables. We propose a piecewise linearization … Read more