A Class Of Evaluation Function Algorithms For Multi-objective Semi-definite Programming

Multi-objective Semi-definite programming, which is a new research field in mathematical programming, is the organic combination of semi-definite programming and multi-objective programming. Because of the great practical application value and rapid development of semi-definite programming, multi-objective semi-definite programming will be a research hotspot.The linear multi-objective semi-definite programming plays an important part in the multi-objective semi-definite programming field. Current method for linear multi-objective semi-definite programming contains the method based on single objective problem and the method based on several single objective problems. In this paper we will introduce a class of evaluation function method——to change linear multi-objective semi-definite programming into single objective semi-definite programming through the introduction of the evaluation function, and then work out it by some interior point method for single objective semi-definite programming.Firstly introduced is the idea point algorithm based on the shortest distance. After presenting the model, we establish the ideal point algorithm with the combination of primal dual path following method in semi-definite programming, and we can finally get a efficient solution. Then we introduce the weighted sum of squares algorithm,the model of which has weighted values. After solving a small scale optimization problem, we establish a one-step algorithm, which gets the new efficient solution starting from the original efficient solution, what is more important, the efficiency has been highly improved.