Research On Two Nonmonotone Optimization Algorithms

In recent years,nonmonotone search technology has been widely concerned by scholars.Using nonmonotone search technique can not only facilitate the algorithm easier to find the optimization solution,but also improve the convergence rate of the algorithm.Therefore,this paper mainly studies two optimization algorithms with nonmonotone search technology,and the main contents are as follows:First,for unconstrained optimization problems,a new adaptive nonmonotone line search strategy is constructed,and a new adaptive nonmonotone Newton algorithm is given combining with Newton algorithm.Under mild assumptions,the global convergence of the algorithm is proved.Numerical experiments show the feasibility and effectiveness of the proposed algorithm.Second,for nonlinear equations,the traditional Levenberg-Marquardt(L-M)algorithm is modified,and a new nonmonotone modified L-M algorithm is proposed by combining nonmonotone line search technology.When the trial step is not accepted,the new algorithm uses nonmonotone line search technology to find the next iteration point,which effectively improves the computational efficiency of the algorithm.Under appropriate assumptions,the global convergence and local convergence of the algorithm are proved.Numerical experiments show the feasibility and effectiveness of the proposed algorithm.The two nonmonotone optimization algorithms proposed in this paper can provide some new ideas for solving unconstrained optimization problems and nonlinear equations effectively,and have certain theoretical significance and application value.