Interior Point Algorithm For The Competitive Market Equilibrium Problems

In this thesis we consider the classic competitive market equilibrium problems of the economics using optimization method.In the first chapter of this thesis we introduce the economic history, background, and the realistic meaning of study of the competitive market equilibrium problems, and the development of solving these problems applying optimization method especially interior point algorithm. In the latter we emphasisly introduce Fisher model and Arrow-Debreu model of Walras theory and their mathematics descriptions, then in the preliminary knowledge introduce the latest interior point algorithm for solving linear programming, give four kind different path-following interior point algorithms. In the second chapter we appropriately modify the interior point algorithm of linear programming, according to the characteristics of market equilibrium problem, and design new primal-dual path-following interior point algorithm for Fisher model, in the first section we introduce and prove primal-dual path-following interior point algorithm proposed by Ye firstly, the computational complexity of the algorithm is better than all former algorithm, in the second and third section we design new primal-dual path-following interior point algorithm by adjusting the step size and search direction, then give detailed theoretical analysis and proof to each algorithm, theoretically the algorithm 2.2, 2.3 is better than Algorithm 2.1. In the last chapter, we analyze how to find the start point, and give some techniques of the implementation of algorithms, also do some computational exercises.