Research On Neural Network Method For Solving Nonlinear Maximin Problem

As we all know,maximin problems play an important role in many optimization fields,and many decision-making problems can be transformed into maximin problems.Therefore,the research on how to solve the maximin problem has certain theoretical value and practical application value.Since the traditional methods for solving maximin problems have exposed more and more shortcomings,people began to find new methods and new ways to solve maximin problems more effectively.Because of the large-scale parallel processing and fast convergence of the neural network,it provides a new way to solve the optimization problem.Therefore,more and more scholars pay attention to using the neural network method to solve the maximin problem.In this paper,two kinds of neural network methods for solving nonlinear maximin problems are introduced,and the corresponding neural network model for solving them is established.The full text is divided into five chapters.Chapter 1 mainly introduces the model of nonlinear maximin problem,the scientific background and research progress of optimizing neural network,the research status and main research contents of maximin problem based on neural network model.The second chapter is the preparatory knowledge.This paper mainly introduces the dynamic system related to the neural network model,the optimality condition of optimization problem,the stability theory of differential equation,LaSalle invariant set and maximum entropy function theory.In Chapter 3,a neural network method based on Lagrange multiplier method for unconstrained nonlinear maximin problems is studied.Firstly,the unconstrained nonlinear maximin problem is transformed into a general constrained optimization problem.Then the corresponding neural network model of the nonlinear programming problem is constructed by using Lagrange multiplier method.Finally,the stability of the established neural network model is analyzed and a specific example is given.In Chapter 4,we study the maximum entropy based neural network method for solving nonlinear maximin problems with inequality constraints.Firstly,the non-differentiable non-linear maximin problem is transformed into equivalent minimization problem by maximum entropy method.Then,the corresponding neural network model is constructed based on Lagrange multiplier method.Finally,the a stability of the established neural network model is analyzed,and a specific example isgiven.The fifth chapter is the comparison and summary of the neural network methods in the previous two chapters,pointing out the problems that we need to further study.