Abstract: Based on modified quasi-Newton equation, a new limited memory quasi-Newton method with two-loop recursion was proposed. Comparing to the classical limited memory BFGS method, the new method uses more function value and gradient informations to construct the quasi-Newton update mectrix, and does not need more computational efforts. The theory analysis and numerical results show the efficiency of the proposed method.

Key words: limited memory method, large scale optimization, modified quasi-Newton equation, limited memory method, large scale optimization