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Several Kinds Of Conjugate Gradient Methods For Solving Nonsmooth And Smooth Optimization Problems

Posted on:2019-07-16Degree:MasterType:Thesis
Country:ChinaCandidate:C N LiFull Text:PDF
GTID:2370330545967758Subject:Operational Research and Cybernetics
Abstract/Summary:PDF Full Text Request
The optimization problem is a widely applied discipline,and the conjugate gradient method is a kind of commonly used algorithm to solve the optimization problem.The optimization problem often discusses the optimal solution to the decision problem and seeks the best calculation method,and studies the theoretical and practical calculation of the calculation method.It is widely used in engineering design,economic planning,production management,transportation,defense and other fields.Common methods of solving unconstrained optimization problems include Newton method,quasi-Newton method,steepest descent method,conjugate gradient method,trust region method and so on.In this paper,we study the conjugate gradient method for solving nonsmooth and smooth optimization problems.Based on the study of solving unconstrained problems,a modified Liu-Storey conjugate gradient method is proposed in this paper,and a Moreau-Yosida regularization technique is combined to convert the original nonsmooth problem into a smooth one.The problem focuses on analyzing the theoretical properties such as its full descent and global convergence.The final numerical results also show that the new algorithm can solve the high-dimensional non-smooth problem.In solving the problem of smoothness,this paper proposes an improved Polak-Ribiere-Polyak method and cites a better line search:improved Weak Wolfe-Powell line search technology.The search technology makes the convergence of the original technology better,and has a better numerical performance.The new method has the following advantages:(1)The algorithm has trust region properties and sufficient descent;(2)Under certain conditions,the global convergence of the algorithm can be obtained;(3)Experimental results show that the algorithm is effective.
Keywords/Search Tags:unconstrained optimization, Conjugate gradient method, inexact line search, global convergence
PDF Full Text Request
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