Several Kinds Of Methods For Solving Bound Constrained Optimization Problems

This thesis is concerned with numerical methods for large-scale bound constrainedoptimization and their convergence properties and performance. Both of the spectralprojected gradient method and the limited memory quasi-Newton method can solvebound constrained optimization problems, but they are of slow convergence or requirelarge amount of calculations etc. To overcome these shortages, we explore conjugategradient method and improve the existing limited memory method to solve large-scale bound constrained problems, and analyze the global convergence of the proposedmethods under mild conditions. In Chapter1, we simply introduce the significanceand the survey on this thesis.In Chapter2, we study the conjugate gradient method for nonnegative constrainedoptimization. By employing the subspace strategy in the classic LS conjugate gradientmethod, we propose a feasible LS conjugate gradient method for solving nonnegativeconstrained optimization problems. The method can not only greatly saves storages,and also saves calculations because it uses Armijo search and need not solve additionalsubproblems.In Chapter3, we study the conjugate gradient method for general bound con-strained optimization. As is known to all, there exist some difcult when the conjugategradient method is used to solve constrained problems and the relevant achievementis very few. In this chapter, we extend the conjugate gradient method proposed inchapter2to bound constrained optimization and establish its global convergence un-der mild conditions. The advantage of the method is that it requires less storagesand calculations. Numerical experiments show that the proposed method has betternumerical results than the existing methods.In Chapter4, we study the limited memory quasi-Newton method for solvingbound constrained problems. Through improving the existing subspace limited memoryquasi-Newton method we present an accelerated algorithm and establish its globalconvergence. Its advantage is that it not only globally converges at express speedunder weaker conditions, and also the projection search is easy to realize.