Three-term Conjugate Gradient Methods For Large-scale Unconstrained Optimization

With the advent of the era of big data,many optimization models are high dimen-sional and complex.Therefore,it is necessary to propose more effective algorithms to solve large-scale unconstrained optimization.Conjugate gradient method is one of the most effective algorithms for unconstrained optimization,and it has been one of the research hotsopts in the field of optimization.This thesis focuses on introducing ran-dom parameters into the three-term conjugate gradient method and applying it to solve large-scale unconstrained optimization.The specific content is as follows:Firstly,a class of three-term conjugate gradient algorithm with random parameters is proposed.The search direction is determined by the search direction matrix with Dai-Liao conjugacy parameters,and a random method for determining Dai-Liao conjugacy parameters is given.Then the search direction generated by the algorithm has suffi-cient descent property.In this thesis,the global convergence of the algorithm is proved under the assumption of uniformly convex function and general function,respective-ly.Numerical results show that the algorithm is effective for large-scale unconstrained optimization.Secondly,for the above three-term conjugate gradient method,a restart factor is introduced and the restart three-term conjugate gradient method with random parame-ters is proposed.Under the assumption that the objective function is uniformly convex function,the global convergence of the algorithm is established.Numerical experiments show the effectiveness of the algorithm.Finally,on the basis of summarizing the main work of this thesis,some problems for further study are proposed.