Quadratic Semi-definite Programming With Mixed Constraints Of Two Kinds Of Algorithms

For the quadratic semi-definite programming with equality and inequality constraints, the interior point algorithm and the quasi-feasible interior point algorithm are given, the duality theory and the optimality conditions of quadratic semi-definite programming are studied, the feasibility and the convergence of the algorithms in this paper are proved. The specific contents are as follows:The first chapter introduces some necessary and essential knowledge of the q-uadratic semi-definite programming, constructs the duality theory and gives the K-KT optimality conditions of the programming with mixed constraints. They are the theoretical foundations for the study of the algorithm in this paper.For the quadratic semi-definite programming with mixed constraints, the barri-er is introduced to the objective function and then the corresponding Lagrangian is given, the constraint problem is converted to unconstraint problem, so the interior point method is given and the convergence of it is proved. Finally, the numerical experiment shows that the algorithm can be used to solve the quadratic semi-defin ite programming of this form and this algorithm is executable.For the quadratic semi-definite programming with mixed constraints, the quasi-feasible interior point algorithm is given in the third chapter. This algorithm requi-res that all iteration points are strictly feasible for inequality constraints. So it is more suitable than the general interior point algorithm for solving such problem. Under certain assumptions, its global convergence is proved.