Curvilinear Paths with Nonmonotonic Inexact Line Search Technique for Unconstrained Optimization
Received:March 11, 2002  
Key Words: Curvilinear paths   preconditioned trust region methods   nonmonotonic technique.  
Fund Project:Supported by National Science Foundation of China (10071050), Science Founda-tion of Shanghai Technical Sciences Committee (02ZA14070), Science Foundationof Shanghai Education Committee (02DK06)
Author NameAffiliation
ZHU De-tong Dept. of Math.
Shanghai Normal University
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      In this paper we modify approximate trust region methods via three preconditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path. In order to accelerate the preconditional conjugate gradient path, we use preconditioner to improve the eigenvalue distribution of Hessian matrix. Based on the trial steps produced by the trust region subproblem along the three curvilinear paths providing a direction of sufficient descent,we mix a strategy using both trust region and nonmonotonic line search techniques which switch to back tracking steps when a trial step is unacceptable. Theoretical analysis is given to prove that the proposed algorithms are globally convergent and have a local superlinear convergent rate under some reasonable conditions. The results of the numerical experiment are reported to show the effectiveness of the proposed algorithms.
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