On the Barzilai and Borwein choice of steplength for the gradient method. (English) Zbl 0778.65045

Raydan, Marcos

IMA J. Numer. Anal. 13, No. 3, 321-326 (1993).

Summary: J. Barzilai and J. M. Borwein [ibid. 8, No. 1, 141-148 (1988; Zbl 0638.65055)] presented a new choice of steplength for the gradient method. Their choice does not guarantee descent in the objective function and greatly speeds up the convergence of the method. They presented a convergence analysis of their method only in the two-dimensional quadratic case. We establish the convergence of the Barzilai and Borwein gradient method when applied to the minimization of a strictly convex quadratic function of any number of variables.

MSC:

65K05	Numerical mathematical programming methods
90C20	Quadratic programming
90C25	Convex programming

Keywords:

choice of steplength; gradient method; convergence; strictly convex quadratic function

Citations:

Zbl 0638.65055