Sensitivity Analysis In Semidefinite Programming

Semidefinite programming(SDP) is an extension of linear programming, It isa new research field in mathematical programming. In recent years,the interiorpoint method was extended to the filed of semidefinite programming, the theoryand algorithm for SDP have developed greatly, and its numerous applicationsare found in combinatorial optimization, cybernetics, system engineering, mobilecommunications.This paper is divided into five parts. In the first part, We introduce thedevelopment and application of the semidefinite programming, summarize somemain thoughts and methods on solving semidefinite programming. In the secondchapter, We introduce some knowledge which we'll use after, including relevantconcepts, duality theory and interior point algorithm on semidefinite program-ming,and sensitivity analysis on linear programming. In the third chapter, westudy sensitivity analysis in semidefinite programming using interior-point meth-ods, And we give numerical examples. In the forth chapter, We develop an imple-mentation of the genericε- sensitivity analysis under perturbations of either theright-hand side or the cost parameters. At last, The paper is concluded.