Several Kinds Of Penalty Function Methods And Their Applications

The penalty function method is a kind of common and very effective method for constrained optimization problems,among which the classical methods include external penalty function method,internal penalty function method,augmented La-grangian method and L1 penalty function method,etc.In this paper,we mainly study the generalized augmented Lagrangian method for the case that the con-strained optimization problem is nonsmooth,and propose the smoothing general-ized augmented Lagrangian algorithm,and apply this conclusion to the semi-infinite programming problem.In addition,for the case that the feasible region of the con-strained optimization problem may be empty,we summarize a kind of generalized unified penalty function framework.Under the framework,a class of penalty algo-rithms with possible infeasibility is presented.The main contents of this article are as follows.The first chapter is the introduction part.Firstly,the research background and current situation of penalty function method are briefly introduced.Secondly,we introduce the research significance and main research content of this paperIn Chapter 2,for nonsmooth constrained optimization problems,we provide a generalized augmented Lagrangian method.In order to find a stable point of nonsmooth constrained optimization problems,we prove that when the penalty pa-rameters are bounded,any accumulation point of the iterative sequence generated by the algorithm is a stable point of the problem.Then,under appropriate con-ditions,the method is applied to the semi-infinite programming problem,and the availability of the algorithm is illustrated by numerical experiments.In Chapter 3,in the case of infeasible problem,a classical L1 penalty func-tion method with infeasible detection is proposed,and the validity of its infeasible detection is proved,and the relevant numerical experiments are given.In Chapter 4,on the basis of the third chapter,we propose a kind of unified penalty function framework,including augmented Lagrangian penalty function,clas-sical L1 penalty function,low-order penalty function,approximate penalty function as special cases.Under appropriate conditions,we prove that this kind of penalty function method can effectively detect infeasibility.