The Solving Constraints Programmong Of Two Nonlinear Lagrange Functions

Nonlinear Lagrange functions is a classic Lagrange function of the amended form, in which the multiplier vectors or constraint functions are involved in nonlinear ways. The dual methods are developed for solving optimization problems based on nonlinear Lagrangians, which is called Nonlinear Lagrange Methods.It play an important role in solving constrained optimization problems .As the nonlinear Lagrangians can be used to develop dual algorithms for nonlinear programming, which require no restrictions on the feasibility of primal variables. This article mainly discusses a kind of Lagrange function for solving nonlinear programming with both inequality constraints and equality constraints.Based on it, dual algorithm is developed.The main contents in this dissertation may be summarized as follows:The first chapter introduces the classic Lagrange function, and pointed out its advantages and disadvantages, and describes the basis of the shortcomings, many scholars have given function effectively to solve non-convex problem.The second chapter describes a well-established inequality constraints, but also equality constrained nonlinear optimization problem of the nonlinear Lagrange function, fist ,it give a number of assumptions in order to guarantee the convergence of the algorithm non-linear Lagrange.Convergence theorem show: When the penalty parameter is greater than a certain threshold value, based on the function of the dual nature of the local convergence algorithm, adjusting the parameters and make them become and, respectively, can be constrained optimal solution.Then, based on the function, the establishment of the corresponding dual algorithm.The third chapter is devoted to an inequality constrained nonlinear optimization problem of nonlinear Lagrange function and its dual algorithm, we first give a number of assumptions in order to guarantee the convergence of the algorithm non-linear Lagrange, these conditions on the development of the corresponding dual Theory is essential.convergence theorem that: when the penalty parameter is greater than a certain threshold value, based on the function of the dual nature of the local convergence algorithm, so that each tends to adjust parameters can be constrained optimal solution.to out the function of the dual function and dual problem, and prove the duality theorem and the saddle point theorem.Finally, the function of the numerical results,It compares the merits of some of these functions, and to give this function with respect to the issue of algorithm wong3 procedures.