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Theory of algorithms for unconstrained optimization. (English) Zbl 0766.65051
Acta Numerica 1992, 199-242 (1992).
[For the entire collection see Zbl 0745.00007.]
The author describes recent theoretical advances in practical methods for unconstrained optimization, e.g. the conjugate gradient method, the BFGS variable metric method, the partitioned quasi-Newton method for large scale optimization, the limited memory BFGS method for large scale optimization, Newton’s method, the Nelder-Meade method for problems with noisy functions. Open questions with respect to global convergence are formulated.
Reviewer: J.Guddat (Berlin)

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C06 Large-scale problems in mathematical programming