Description For The Optimality Conditions Of Conic Optimization

In Nonlinear Programe, the conditions that the optimal solution satisfied are very important. They provide needful theoretical foundation for derivation and calculation of all kinds of algorithms. In rencent year, Conic Optimization is very popular field of optimization. This article focuses on summing up and investigation of Conic Optimization.ChapterⅡof this article sets the definitions of cone and second order cone, then investigates the tangent cone,second order tangent set and algebraic properties of a second order cone. This article sums up description for the classical optimization, and investigates several important constraint qualifications and the relationship among them.ChapterⅢof this article firstly introduces the first and second order optimal condition of general conic optimization. SOCP was proposed early, however, the intensive study occur in rencent decades. With the extensive use of SOCP in application area such as computer, more and more researchers begin to investigate SOCP. This article investigates the first order and second order optimal conditions of SOCP after introducing that of general conic optimization.