Multiplier Method With A New Class Of NCP Function

Constrained nonlinear programming problems are widely used in the field of natural science, economy, engineering field. So, exploring the research methods for solving constrained nonlinear programming problem has already become the trend of research in the field of new optimization.In recent years, research on the development of this direction quickly, creating many new algorithms, such as, the penalty function method, the extended Lagrange filter algorithm, trust region algorithm, QP-free algorithm and the study of multiplier method etc.There will be a method for constrained nonlinear programming problem is transformed into an unconstrained problem of solution of the constrained nonlinear programming problem.That is to say with a sequence of unconstrained sub problem instead of the original constrained problem.Multiplier method belongs to this category method, also called the augmented Lagrange function method. Combining the objective function and constraint function to construct augmented Lagrange function for solving constrained problems.When, C and D are sufficiently large, there is a nice equivalence between the unconstrained optimization and the primal constrained problem.Hestenes and Powell separately proposed approximate augmented Lagrange function for solving equality constrained nonlinear optimization at first. Approximate augmented Lagrange function is extended to the optimization problem with inequality constraints by Rockafel. Then obtained the augmented Lagrange function optimization problems with general constraints, called classic augmented Lagrange function. This paper presents a multiplier method with inequality constraint programming problem,put the inequality constraints into equality constraints.And proposed the corresponding algorithm. It proves that the method discussed the convergence and local optimal solution and the global optimal results under suitable assumptions.The first chapter, introduces the general situation of some of the basic knowledge and research methods of nonlinear programming.Then introduce the property of NCP function.The second chapter, proposes a augmented Lagrange functions with F-B NCP function. In appropriate assumptions discussed it’s properties and proved its equivalence with the original question. Also gives the algorithm and show that the algorithm’s convergence.The third chapter, constructing a new nonlinear complementarity(NCP) function based on the F-B NCP function, then construct Dipillo Lagrange multiplier function to obtain the solution of the original problem.The fourth chapter, in addition to the F-B NCP nonlinear complementarity function outside, analyzes the properties of the 3-piecewise and 4- piecewise linear NCP functions.The fifth chapter carries on the summary and the forecast to this article.