Self-Adaptive Limited-Memory Quasi-Newton Method with Function Value Information for Large-Scale Unconstrained Optimization

We extend the modified BFGS algorithm to a limited-memory framework, and propose a self-adaptive limited-memory quasi-Newton method, denoted as LADBFGS, for large-scale unconstrained optimization. The proposed method fully exploits function value information to improve the curvature approximation of the objective function, while enabling dynamic and adaptive adjustment of parameters. We establish the global R-linear convergence of the proposed algorithm for uniformly convex problems. Numerical experiments on 102 standard unconstrained test functions with dimensions of no less than 1000 show that the proposed LADBFGS method outperforms the standard limited-memory BFGS method in terms of iteration count, number of function and gradient evaluations, and computational time, and also achieves a higher success rate for solving the test problems.