A DISJUNCTIVE CUTTING PLANE ALGORITHM FOR BILINEAR PROGRAMMING

In this paper, we present and analyze a finitely convergent disjunctive cutting plane algorithm to obtain an \epsilon -optimal solution or detect the infeasibility of a general nonconvex continuous bilinear program. While the cutting planes are obtained like Saxena, Bonami, and Lee [Math. Prog., the algorithm that guarantees finite convergence is exploring near-optimal extreme point solutions to a current relaxation at each iteration. In this sense, the presented algorithm and its analysis extend the work Owen and Mehrotra [Math. Prog., 89 (2001), pp. 437--448] for solving mixed-integer linear programs to the general bilinear programs.