Research And Application Of Non-monotonic Trust Region Algorithm

With the rapid development of economy and the whole world,the theories and methods of optimization are updated and developed.At the same time,various optimization theories have been applied rapidly and deeply in the fields of economic management and engineering.Since Grippo put forward the non-monotone optimization method in the 1980s,this idea and method began to emerge.Many scholars in various countries have carried out research on this topic and have published a series of papers,which has enriched the non-monotone optimization method.This paper mainly studies the theory and algorithm of non-monotonic trust region optimization method,and applies the theory and algorithm to the parameter estimation of the Lorenz curve fitting model and the optimization design of MRO problem in engineering.At first the thesis introduces the theory and development of nonlinear programming,trust region method,derivative free optimization,quality control theory,the Lorenz curve and nonmonotone technology.Based on the further development of these techniques and algorithms,and the thesis puts forward the improved trust region algorithm and its application in the field of the Lorenz curve and chemical engineering.Firstly,an improved non-monotonic trust region algorithm is designed by combining the characteristics of two kinds of non-monotonic algorithms,namely the average type algorithm and the extremely large type algorithm.At the same time,the corresponding numerical experiments are carried out and the results are satisfactory.Derivative free optimization is a hot topic at present.Based on the research results of previous scholars,an improved non-derivative trust region algorithm is proposed and analyzed,and the convergence result is obtained.Secondly,this paper mainly discusses the properties that must be satisfied by lorentz curve fitting model,puts forward the construction method,and constructs a family of lorentz curve expressions.For the parameter estimation problem in the model,the improved trust region algorithm is proposed to calculate the parameters,and the corresponding parameter values are obtained.Combined with the income statistics of some countries and regions,our Lorenz curve model and some other models are compared and calculated,and the statistical indexes are better.Combined with the quality control theory,aiming at the problems of chemical product production in industrial engineering,the relevant optimization model and algorithm are put forward.With specific data,the relevant calculation and statistical analysis by the improved non-monotone trust region algorithm and the non-monotone derivative-free trust region algorithm,the overall desirability index has been significantly improved.The main innovations of this paper are as follows.Firstly,the non-monotone technique in nonlinear programming is studied,and an improved non-monotone trust region algorithm is proposed.Secondly,combining with the research results of scholars in the previous stage,an improved derivative free trust region algorithm is proposed and analyzed,and the corresponding convergence result is obtained.Thirdly,combining the properties and geometrical characteristics of the Lorenz curve,this paper puts forward the construction method,obtains the expression of a new family of the Lorenz curve.The improved non-monotone trust region algorithm is used to calculate the model parameters.With the data of relevant literature to calculate,the statistical indexes are significantly improved.Fourthly,according to the theory of management,quality control theory and nonlinear programming,specific analysis and the corresponding optimization model are established for industrial engineering production problem.The improved non-monotone trust region algorithm is used for computing and significant improvement of the value of overall desirability function is obtained.