New adaptive stepsize selections in gradient methods. (English) Zbl 1161.90524

Frassoldati, Giacomo; Zanni, Luca; Zanghirati, Gaetano

J. Ind. Manag. Optim. 4, No. 2, 299-312 (2008).

Summary: This paper deals with gradient methods for minimizing \(n\)-dimensional strictly convex quadratic functions. Two new adaptive stepsize selection rules are presented and some key properties are proved. Practical insights on the effectiveness of the proposed techniques are given by a numerical comparison with the Barzilai-Borwein (BB) method, the cyclic/adaptive BB methods and two recent monotone gradient methods.

MSC:

90C52	Methods of reduced gradient type
90C20	Quadratic programming
65K05	Numerical mathematical programming methods
65K10	Numerical optimization and variational techniques

Keywords:

unconstrained optimization; strictly convex quadratics; gradient methods; adaptive stepsize selections