Applications Of Lasserre Relaxation Method In Nonlinear Programming Problems

Lasserre relaxation method is an important method for solving polynomial optimization problems. The method can generate a convergent sequence which may approach global optimal solutions of poly-nomial optimization problems infinitely. Since Lasserre relaxation method is excellent in theory and polynomial optimization problems can be applied in motion control system, biological system etc., the method recently became a research hot spot in optimization field.This paper mainly discussed how to apply Lasserre relaxation method in the sequential quadratic programming method and trust region method to solve nonlinear programming problems with general constraints.In Chapter 1, we introduced Lasserre relaxation method, software GloptiPoly3 and the main con-tents of the paper.In Chapter 2, a sequential quadratic programming method solving nonlinear programming prob-lems with general constraints was proposed, in which Lasserre relaxation method was applied to solve its subproblems. We analysed convergence of the method. Numerical experiments show that the method is efficient for solving nonlinear programming problems with general constraints. In terms of the ac-curacies of numerical results, there are good consistencies between the new method and the software package fmincon in MATLAB. At the same time, we can see that the computing time of the former is more than the latter's.In Chapter 3, we proposed a trust region method whose subproblem is solved by Lasserre relaxation method. Convergence of the method was analysed. We gave highlighted discussions on numerical performance of the method. In terms of the accuracies of numerical results, there are good consistencies between the new method and the software package fmincon in MATLAB.Meanwhile, the computing time of the former is more than the latter's.The paper made a brief summary at the end.