Abstract: In this paper, objective function value information is exploited in limited memory BFGS-type algorithms. we first construct a new quadratic function satisfying some interpolation conditions to approximate the objective function, get a new weak secant equation. Combining the new weak secant equation and that obtained by Yuan\cite{yuan1991}, a class of limited memory BFGS--type algorithms including the classic LBFGS algorithm based on a new weak secant equation are proposed. The convergence of this class limited memory BFGS-type algorithms is proved. Numerical results for standard test problems from CUTE are reported, which indicate that all the algorithms in the proposed class perform quiet well.

Key words: unconstrained optimization, weak secant equation, LBFGS algorithm, convergence analysis, limited memory