解线性等式约束优化问题的模式搜索过滤集方法

提出一个解线性等式约束无导数优化的模式搜索过滤集算法,该算法将过滤集技术嵌入无导数优化算法中以改善算法的效率. 建立了新算法的总体收敛性, 初步的数值试验结果表明新算法是有效的.     

A trust region algorithm for a class of nonlinear optimization

Abstract. This paper presents a trust region algorithm for nonlinear optimization with linear in-equality constraints. The global convergence of the algorithm is proved. Local quadratic con-vergence is obtained for a strong local minimizer.     

CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUTSUFFICIENT DECREASE CONDITION

1IntroductionOurproblemistominimizeafllnctionofnvariables,wheref:R"~R',fECZalldgdenotesthegradientoff.Problem(1)isoftellsolvedbyvaxiouscolljugategradientmethodsofthefornl:wherePhisascalar,andAhisastepsizechosenbymeansofolle-dimentiollalsearcllrules.VariousconjugategradientInethodsarecharacterizedbydifferentchoiceofPh,thebestkllowllforlllulaeforPharecalledtheFletcher-Reeves(FR),Polak-Ribiere(PR),alldHestenes-Stiefel(HS)forlrmlar,andarerespectivelygivenbyThecolljugategradientlllethodcor…     

A NEW GRADIENT PROJECTION METHOD AND ITS CONVERGENCE

In this paper, by using a new projection, we construct a variant of Zhang's algorithm and prove its convergence. Specially, the variant of Zhang's algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang's algorithm hasn't these properties.