Global Optimization Auxiliary Functions Method And Its Applications In Support Vector Machine

As an important part of global optimization,deterministic optimization algorithms have always been the focus of scholars' research.The difficulty of nonlinear programming is how to find the global minima among many local minima.But the auxiliary function methods can help the objective function jump out of the current local minima to find better local minima.Support vector machines,as a machine learning method,show great advantages in classification and regression,which have aroused great interests from scholars at home and abroad.The main part of this article is divided into six parts,the research focuses on the analysis of support vector machine's Mond-Weir dual based on ?convexity and two types of auxiliary function methods and their applications.The first chapter introduces the research significance and research status of global optimization problems,as well as the research status of filled function method and stationary point auxiliary function method,and then briefly introduces several types of random algorithms and support vector machine problems,and finally explains the auxiliary function method application in practical problems.In the second chapter,we first introduced the problem of constrained support vector machines with sparse variables transformed into an unconstrained optimization problem,and then studied a kind of generalized convexity,namely ? convexity,and proposed the vector function ? function,an example is given to verify the validity of the ? function and the existence of the ? function.Finally,based on the ? convexity,the Mond-Weir dual method is used to optimize the support vector machine problems.In the third chapter,a new type of non-parameter filled function is proposed based on the definition and assumptions of the filled function.The theoretical properties of the function are analyzed and an improved non-parameter filled function algorithm is designed.The Python programming language performs numerical experiments and compared with previous results.It shows that the filled function and algorithm are effective.In the fourth chapter,in order to overcome the problem that the filled function algorithm cannot minimize the auxiliary function at the current local minimum point,a new class of stationary point auxiliary function methods is proposed,the theoretical properties of the function are analyzed,and an improvement is designed.The stationary point auxiliary function algorithm,numerical experiments and compared with other literatures show the effectiveness of the algorithm.In the fifth chapter,most of the previous scholars' researches on auxiliary function methods only focused on theoretical analysis and numerical experiments.This article attempts to use auxiliary function methods to solve practical problems.In the first section,the filled function method is used to process enzymatic reaction data.In the second section,the validity of Newton's cooling law is verified using the stationary point auxiliary function method;in the third section,the iris plant data set is analyzed,and the filled function method is used to solve the classification of iris setosa and iris versicolour.In the sixth chapter,we summarized the research work of this paper,points out the shortcomings of the paper,and makes further prospects for future research directions.In general,this paper mainly constructs a new filled function and stationary point auxiliary function method for unconstrained optimization problems,and conducts theoretical analysis of optimization of support vector machines.The popular algorithmic programming language Python is used to practice corresponding algorithms.Numerical experiments and both the applications on the actual problem show that the auxiliary function method has its superiority in solving some problems.During the research process,it was found that the auxiliary function method has shortcomings in solving the support vector machine problem,so for this kind of problem,the auxiliary function method needs to be further improved research.