Generalized bilinear programming: Part I. Models, applications and linear programming relaxation

The evolution of the bilinear programming problem is reviewed and a new, more general model is discussed. The model involves two decision vectors and reduces to a linear program when one of the decision vectors is fixed. The class of problems under consideration contains traditional bilinear programs, general quadratic programs, and bilinearly constrained and quadratically constrained extensions of these problems. The paper describes how several important applications from the literature, including the multiple modular design problem, can be modeled as generalized bilinear programs. Finally, it derives a linear programming relaxation that can be used as a subproblem in algorithmic solution schemes based on outer approximation and branch and bound.