| The thesis is to study the gradient projection method to solve the convexly constrained optimization problems.This paper is composed of four chapters.Chapter 1 is the introduction of this paper,which introduces the current situation and the main results in this paper.In Chapter 2,wc study the gradient projection method with exact stcpsize rule.Frequently,this rule is not used since it requires expensive computation. However,Harge and Park pointed out for some difficult optimization problcms where the structure of constraints is relatively simple,the exact stcpsizc rule is useful since it provides a mechanism for making a large step to escape from one valley of the cost function and move to another(possibly distant)valley with a small minimum cost.Therefore,it is quite ncccssary to study the convergence of the gradient projection method with exact stcpsizc rule.We prove that the projected gradient of the itcrativc sequence generated by the method converges to zero under certain conditions:In Chapter 3,wc propose a gradient projection method with perturbation to solve the convexly constrained optimization problems.Its iterate formula is xk+1=PΩ[xk+αk(-▽f(xk)+ωk)],whereωk is a perturbation term and satisfies (?)‖ωk‖=0,,andαk is the Armijo stepsizc rule.Wc prove the convergence of the method under certain conditions.The result illustrates that the convergence of gradient projection method is not influenced when the negative gradient direction is perturbed lightly.In Chapter 4,wc study the gradient projection method with generalized Armijo stcpsize rule.The stcpsizc rule is a generalization of Armijo stcpsizc rule.We prove the convergence of the method under certain conditions.Furthermore, we study the finite termination of the method,and get respectively the finite termination under the conditions of weak sharp minima and non-degenerate without the assumption about convexity,that is,the method terminates finitely to a stationary point of the convexly constrained optimization problems.
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