A New Gradient Projection Method With Self-adaptive Step Size And Application

Gradient Projection method is a classic algorithm for solving constrained optimization.It takes the advantage of its low per-iteration cost.However,its efficiency can be affected by the choice of step size.Based upon the classical Gradient Projection method,a new gradient projection method with self-adaptive step size rule is proposed in this paper.On one hand,it does not need the information of objective,and it only requires to clearly understand the gradient information;on the other hand,it can accept longer step size than that based on Armijo rule to accelerate the convergence.The details are organized as follows:The first chapter mainly discusses the background and significance of the selected topic,including the domestic and international research status of the Gradient Projection method,and the compressed sensing theory and so on.The theoretical results will be introduced in the second chapter,involving a new proposed gradient projection method with self-adaptive step size rule.In addition,we design a novel algorithm relying on the objective function chosen as the quadratic function or the general strongly convex function,then analyze its convergence.In the third chapter,we demonstrate that when the objective function is selected as the quadratic function,error bounds of the developed algorithm hold the fast convergence speed at the kO)/1(rate in the case of the residual value and function value.The numerical experimental results are given and validity of the algorithm applied to the compressed sensing is verified in the fourth chapter.The last chapter is a summary of this thesis and comments on the prospect study for the future research.