INTERIOR-POlNT METHODS FOR OPTIMIZATION PROBLEMS IN SOCIAL SYSTEMS

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We have performed a basic research on the interior point methods for solving optimization problems in social systems. In this year, our research mainly devoted to the development of interior point methods for linear programming and semidefinite programming, and devoted to the analysis of the global convergence and the local convergence of these methods.Most of the optimization problems iii social systems could be modeled as mathematical programming problems. The linear programming problem is the most fundamental mathematical programming problem. We performed two important research on the interior-point methods for linear programming. Firstly, in order to speed up the local convergence of interior point methods, we investigated an algorithm which trace the central path in high degree. As a result of this research, we proposed a high order infeasible interior point algorithm. Secondly, we are interested in the problem to get an initial interior point to perform an algorithm, For this purpose, we investigated two self-dual systems for linear programming, which have trivial initial points.We studied not only linear programming, but also convex programming, semidefinite programming, and semi-infinite programming. There are many search directions in interior-point methods for solving semidefinite programming problems. We investigated a self-dual subfamily of such directions. We also studied interior-point methods for solving linear and quadratic semi-infinite programming problems and proposed a dual-parameterization algorithm for convex semi-infinite programming.