An Augmented Lagrangian based Semismooth Newton Method for a Class of Bilinear Programming Problems

This paper proposes a semismooth Newton method for a class of bilinear programming problems (BLPs) based on the augmented Lagrangian, in which the BLPs are reformulated as a system of nonlinear equations with original variables and Lagrange multipliers. Without strict complementarity, the convergence of the method is studied by means of theories of semismooth analysis under the linear independence constraint qualification and strong second order sufficient condition. At last, numerical results are reported to show the performance of the proposed method.