Solving binary semidefinite programming problems and binary linear programming problems via multi-objective programming

In recent years the binary quadratic program has grown in combinatorial optimization. Quadratic programming can be formulated as a semidefinite programming problem. In this paper, we consider the general form of binary semidefinite programming problems (BSDP). We show the optimal solutions of the BSDP belong to the efficient set of a semidefinite multiobjective programming problem (SDMOP). Although finding all efficient points for multiobjective is not an easy problem, but solving a continuous problem would be easier than a discrete variable problem. In this paper, we solve an SDMOP, as an auxiliary, instead of BSDP. We show the performance of our method by generating and solving random problems.