Algorithms Of Linear Programming And Constrained Nonlinear Programming

As for the theory of Optimization and stradegy ,Linear Programmmg and Constrained Nonlinear Programming are two important problem.In accord with present conclussions,the paper has done some furthur and beneficial work in their algorithms.This paper is made up of two sections. In section one, based on theory of n dimensional Euclid space, a new method labeled as "PointLinePlane" Recycling Optimization Algorithm is proposed to solve the linear programming problem . This algorithm is proposed on the basis of the thought as follovvs: as for three dimensional Euclid space, the feasible region of any linear programming problem is a extended convex polyhedron, of which surface is consisted of some planes, and its objective function can be regarded as a parallel plane pencil with objective function value acting as parameter. If some linear programming problem has optimum solution, then there must at least exist such a edge among ali edges passing through some known vertex of feasible region that the objective function value of the other vertex is more optimic than the one of the known vertex, otherwise, the known vertex is the optimum solution of the linear programming problem. Continuing above curse, then we can get its optimum solution, that is to say, starting from some feasible vertex, we will get the optimum solution of some linear programming problem after finite times transition of vertex along edge of feasible region. Spontaneously, it occurs to us whether we could generalize the algorithm from three dimensional é‘‘æ­Ÿ to n dimensional one, this is the academic setting of the "PointLinePlane" Recycling Optimization Algorithm. In contrast to existing Simplex Method, this method has several peculiarities as follows: To begin with, applying it to solve linear programming problem. One needn't introduce any additional variable such as relaxing variable, artificial variable and other parameters, so that calculation is subtracted on a large scale. In addition to this, as a result of its higher degree of structuralization, this algorithm can be more easily transformed into program language and, of course, more quicklyperformed by computers. Moreover, comparing with Simplex Method, this algorithm couldn't cause Vibration Phenomenon . In section two, issue involves how to cakulate the constrained nonlinear programming problem by SUMT and AG .The method overcomes some limitations such as differentiability, continuity or singlepeak of functions etc. Its applying category is more extensive than any other existing methods. Especially, it is very efficient for us to cakulate huge constrained nonlinear programming problems.