Theory of algorithms for unconstrained optimization. (English) Zbl 0766.65051

Nocedal, Jorge

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)

MSC:

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

Keywords:

unconstrained optimization; conjugate gradient method; BFGS variable metric method; quasi-Newton method; large scale optimization; Newton’s method; Nelder-Meade method; global convergence

Citations:

Zbl 0745.00007

Software:

ve08; Algorithm 611; L-BFGS