The Nonmonotone Line Search Technique And Its Applications

Because of its rapid convergence and efficient of getting global optimized solution, the nonmonotone line search technique is strongly favored by many scholars. This thesis focuses on applications of nonmonotone line search technique in solving unconstrained optimization problems and nonsmooth equations. There are four chapters. In the first chapter, we mainly give some basic knowledges and present research histories and situations of solving unconstrained optimization problems and nonsmooth equations. In the second chapter, We proposed a new nonmonotone step size rule and analyze the global convergence of new BFGS quasi-Newton method. The new step size rule is similar to Zhang H.C. nonmonotone step size rule and contains it as a special case. Numerical experiments have been conducted which show that the proposed algorithm is encouraging. In the third chapter,we presents an inexact Newton-Krylov method for solving systems of nonsmooth equations. Global convergence of the proposed algorithms is established under a nonmonotonic backtracking strategy. Numerical examples are given to show the practical viability of these approaches.