Research Of Non-monotone Trust-region Method

In engineering, physics, economics and management and other fields, optimizationtheory is widely used. It has become a very active research topic and an independentdiscipline. According to the optimization problem, the trust region is a good method ofcalculation.Trust region algorithm has the property of strong convergence and strongadaptability. And thus it attracts extensive attention of nonlinear optimization sectors.Especially for nonmontone trust-region method,compared to monotone trust-regionmethod this avoids Maratos effects and reduces the amount of calculation. This methodhas practical application vaue.This paper addresses the nonmonotone trust-region method on the basis of thecurrent scholarship. we summarize the details as follows:The first chapter summarizes the development history the product anddevelopment of trust-region algorithm in particularly. It introduces the initial productprocess and basic conception of this method. Finally it introduces nonmontonetrust-region method and self-adaptive trust-region method.The second chapter discussed the problems of traditional trust region algorithm,the structure of the subproblems, the basic structure of the algorithm, the majorprocess of the method, convergence and global convergence of the algorithm, etc.In the third chapter, we propose an improved nonmonotone self-adaptivetrust-region algorithm for solving the unconstrained optimization. We combinenonmonotone technology with self-adaptive trust-region algorithm from Cui and Wu’sarticle.This avoids Maratos effects and reduces the amount of calculation. Under someassumptions，the effective convergence of the algorithm are established. Preliminarynumerical results show that the new method is efficient for solving unconstrainedoptimization problem.In mathematics programming, constrained optimization problem also accounts fora large proportion. Especially the solution of the nonlinear equations, is also animportant subject. So this chapter puts forward with nonmonotone adaptive trust regionalgorithm for solving nonlinear equations. The first process is to turn equations.Firstly,we should turn the equations into unconstrained optimization problem.Andthen the nonmonotone self-adaptive trust region algorithm is used to solve the nonlinear equations.This paper lists some assumptions. And under the conditions of thehypothesis,the convergence of the algorithm is received.