Studies On Several Algorithms For Nonlinear Constrained Programming

Nonlinear programming problems are widely applied in economics and management,involing resource distribution,the plan of product,market management and network application and so on.In massive engineering technology and automatic programming.Therefore,studying the nonlinear programming has the vital practical significance and application prospect.Nonlinear programming takes of the characteristics of "nonlinear",solving the problem is a challenge one,which has received much attention all the time.The traditional methods have Newton's method,steepest descent method,fessible direction method and trust region method and so on.In recent years,resort to the biology evolution developing some intelligent algorithm such as evolutionary algorithm,particle swarm optimization algorithm.For some problems,they need to combine common method and the intelligent method to solve the relatively difficult nonlinear programming.So this paper will do the further analyze and discussion for nonlinear constrained programming.For this paper,we will make detailed discussion on the solving methods for nonlinear constrained programming.We will discuss three algorithms.The first method is hybrid chaos algorithm,we transforms constrained optimization problem of any number of constraints into a two objective preference optimization problem.In addition, we prove the relationship between the optimization solution of nonlinear constrained programming and the Pareto efficient solution of multiobjective unconstrained programming,which is equivalent.Wang Yuping[ref.1]make the similar transformation and propose the evolutionary algorithms,but which exist some drawbacks such as early convergence,the slow of optimization speed.In this paper we present the Hybrid chaos algorithm,make use of the chaos variable to search,in the course of the second search,applying the steepest descent and rapid getting the satisfied solution.The second algorithm is the modified DFP,firstly the penalty function are made use of for transferring constrained nonlinear programming into unconstrained ones.Extended,the global convergent result proof of the modified DFP method are given.The third algorithm is Dai conjugate gradient method,which is different from others about the choosing of theβ_i,we will make the deeply discussion of this method and show with a numerical example that the Dai conjugate algorithm is efficient.The three algorithms is possibility and efficient for nonlinear constrained programming.