Inside-Ellipsoid Outside-Sphere (IEOS) model for general bilinear feasibility problems: Feasibility analysis and solution algorithm

Abstract

This paper deals with general bilinear feasibility problems. A nonlinear transformation is introduced that reformulates a general bilinear feasibility problem as a Linear Matrix Inequality (LMI) problem augmented with a single non-convex quadratic constraint. The single non-convex quadratic constraint has a regular concave constraint function. Due to the LMI part of this formulation, it is easier to analyze, and we prove that the solution space of this formulation is located inside several ellipsoids and outside a sphere. This leads to our proposed Inside-Ellipsoid and Outside-Sphere (IEOS) model for general bilinear feasibility problems. Then, the feasibility analysis of our proposed IEOS model is performed. The related necessary feasibility conditions and sufficient feasibility conditions are theoretically developed. Moreover, an iterative algorithm for solving our IEOS model is also proposed.Two applications including matrix-factorization problem in control systems and power-flow problem in power systems are considered to evaluate the practicality of our proposed approach. Both problems are formulated as IEOS models. It is shown that our proposed model can provide more accurate solutions to these problems as compared to previous competing approaches in the relevant literature.