Nonlinear Optimization Problems For A Class Of Memoryless Non-quasi-newton Algorithm Research

Seeking fast theoretical convergence and effective algorithms in unconstrained optimization is a very interested research topic for the optimization specialists and engineers, non-quasi-newton methods and conjugate method have been proved to be two of the most efficient methods when applied to unconstrained optimization by the favorable numerical experience and theoretics. It. also show clear superities that it is not necessary to compute hessian matrix, only need the gradient. Decent direction can be resulted when the hessian matrix is positive. It has been shown that the iterates generated by broyden class except the DFP method has superline convergence[ll,26,27,28,29], and has n-step convergence rate. The disadvantages of quasi-Newton algorithm is the great memory,so for large problems, memory difficulties may be encountered.The basic idea of the conjugate gredient methods is the combination of the conjugation and the most rapid decline method.It involves less memory and has secondary termination and effective numerical performance. However, when the function is the general nonlinear function,even under the exact line search,the convergence of the conjugate gredient methods can hardly be got. Consider the advantages and disadvantages of the above two algorithms,paper [3] gives a class of memoryless non-quasi-newton algorithm about unconstrained optimization. Compared the conjugate gredient method for unconstrained optimization, memoryless non-quasi-newton algorithm has not much increased whether in memory or each iterative calculations,but its numerical performance is much better than the conjugate gradient methods.Based on the non-quasi-newton equation, combining the memoryless non-quasi-newton algorithm in paper [3], we give a new class of algorithm for unconstrained optimization.numerical experiments indicate that this algorithm is very effective, particularly for solving large-scale optimization problems.In chapter 1 , we first introduce the development of optimization and some extensive optimality conditions which to decide the optimum solution. We review...