On the limited memory BFGS method for large scale optimization. (English) Zbl 0696.90048

The authors investigate the numerical performance of several optimization algorithms for solving smooth, unconstrained and in particular, large problems. They compare their own code based on limited BFGS-updates with the method of A. Buckley and A. LeNir [ACM Trans. Math. Software 11, 103-119 (1985; Zbl 0562.65043)], which requires additional conjugate gradient steps, with two conjugate gradient methods and with the partitioned quasi-Newton method of A. Griewank and Ph. L. Toint [in: Nonlinear optimization, NATO Conf., Ser., Ser. II, 301-312 (1982; Zbl 0563.90085); Math. Program. 28, 25-49 (1984; Zbl 0561.65045) and Numer. Math. 39, 429-448 (1982; Zbl 0505.65018)]. The results are based on 16 test problems where the dimension varies between 50 and 1000. Conclusions of the numerical tests are that the method of the authors is faster than the method of Buckley and LeNir with respect to number of function evaluations and execution time. The method also outperforms the conjugate gradient methods and is competitive to the partitioned quasi- Newton method on dense problems, but inferior on partitioned problems. Moreover scaling effects are evaluated and a convergence analysis for convex problems is presented.
Reviewer: K.Schittkowski


90C30 Nonlinear programming
90C06 Large-scale problems in mathematical programming
65K05 Numerical mathematical programming methods
90C52 Methods of reduced gradient type
Full Text: DOI


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