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A Nonmonotonic Trust Region Algorithm with Line Search

Shujie Jing

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Abstract

A nonmonotonic trust region algorithm with line search for unconstrained optimization problems is presented in this paper.Its global convergence and Q-quadratic convergence are proved under suitable conditions.Differing from usual nonmonotonic trust region method,the algorithm takes line search technique to get the next iterative point when the trail step is not accepted.This method may not only reduce a considerable saving,but also avoid the possibility that the reference function value may be much larger than the real one.

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What this paper is about

A nonmonotonic trust region algorithm with line search for unconstrained optimization problems is presented in this paper.Its global convergence and Q-quadratic convergence are proved under suitable conditions.Differing from usual nonmonotonic trust region method,the algorithm takes line search technique to get the next iterative point when the trail step is not accepted.This method may not only reduce a considerable saving,but also avoid the possibility that the reference function value may be much larger than the real one.

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Available abstract

A nonmonotonic trust region algorithm with line search for unconstrained optimization problems is presented in this paper.Its global convergence and Q-quadratic convergence are proved under suitable conditions.Differing from usual nonmonotonic trust region method,the algorithm takes line search technique to get the next iterative point when the trail step is not accepted.This method may not only reduce a considerable saving,but also avoid the possibility that the reference function value may be much larger than the real one.

Key concepts: Trust region, Line search, Convergence (economics), Algorithm, Line (geometry), Mathematical optimization, Function (biology), Point (geometry)

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