A Study On Nonmonotonic Trust Region Algorithm For Semidefinite Programming

In recent years, Semidefinite programming (SDP) has become a very importantresearch field in mathematical programming. SDP is an extension of linear programming,its theory and algorithm have developed greatly, and it is widely used in combinatorialoptimization, system engineering and electrical engineering.A nonmonotonic trust region method is proposed for solving the SDP problems. Themain work includes the following two aspects:The equivalent smoothing equations of the optimal condition are obtained byexploiting the Fischer-Burmeister function that is extended to the matrix domain, andthe center of the path of SDP is rewritten, at the same time, the equations provedLipschitz continuous and differentiable in theory. Thus the nonmonotonic trust regionalgorithm for solving SDP problems is constructed.The convergence of the algorithm isanalyzed theoretically.Some numerical results indicate that the proposed method isefficient.In order to avoid the optimal solution is locally optimal solution when the initialsearch point near the canyon, this paper amends the trust region radius correctionconditions, thus a new nonmonotonic trust region algorithm for solving SDP problems isconstructed. Convergence analysis of the algorithm is given. Numerical results showthat the algorithm is effective in solving SDP and it is superior than exist algorithms.