Research On Sparse Quasi-Newton Method And Its Application

In this paper, we propose three new quasi-Newton methods for unconstrained optimization. The main content of the thesis is presented as follows:In chapter two, based on new quasi-Newton equation, we propose new quasi-Newton method combining with BFGS-type update formula. Under some assumptions, we proved the global convergence and the speed of super linear convergence. Numerical results show that the method is effective.In chapter three, based on the quasi-Newton equation, together with non–monotone line search skill, we designed a new diagonal-sparse quasi-Newton method with modified Grippo non-monotone line search for unconstrained optimization. The global convergence and super linear convergence are guaranteed to our new method, meanwhile, in every iteration, the new step size generated by the new method is lager than that of Grippo non-monotone line search. Numerical experiments show that the new method is effective and suitable for large scale problems.In chapter four, on the base of new quasi-Newton equation, together with modified non-monotone line search skill, we designed new diagonal-sparse modified quasi-Newton method with modified Grippo non-monotone line search for unconstrained optimization. Global convergence and super linear convergent speed of the method are proved. Numerical experiments show that the new method is effective and suitable for large scale problems.