The Study Of Properties And Algorithm For Several Classes Of No-linear Convex Programming

In this paper,the author introduces the properties and algorithms of three classes of convex programming.The algorithms have a common character,which all the algorithm use the K-T condition to transform the model of programming.These content is introduced in two chapters.In this paper,it has two innovations:one is that the author uses the simplex method to solve the bi-level linear convex programming;the other is that uses the Frank-Wolfe algorithm to solve the bi-level no-linear convex programming.In chapter l,it introduces the preparatory knowledge.In chapter 2,it studies the properties and algorithm of convex quadratic programming.First,it studies the properties,and uses the K-T condition to transform the model of convex quadratic programming,then uses the complementary pivoting algorithm to solve the programming.In chapter 3,it studies the properties and algorithm of convex bi-level programming.Firstly,it studies the properties;Secondly,it introduces the properties and steps for transforming the model of linear bi-level programming,and find the solutions of linear bi-level programming by simple method;Lastly,it introduces the algorithm of a class of no-linear bi-level programming,which is different to the linear bi-level programming,the just difference is that the objective function is convex quadratic function,not linear function.Similarly,use the K-T condition to transform the model,and get the solution by Frank-Wolfe algorithm.