Inexact spectral projected gradient methods on convex sets. (English) Zbl 1047.65042

Birgin, Ernesto G.; Martínez, José Mario; Raydan, Marcos

IMA J. Numer. Anal. 23, No. 4, 539-559 (2003).

Authors’ abstract: A new method is introduced for large-scale convex constrained optimization. The general model algorithm involves, at each iteration, the approximate minimization of a convex quadratic on the feasible set of the original problem and global convergence is obtained by means of nonmonotone line searches. A specific algorithm, the inexact spectral projected gradient (ISPG) method, is implemented using inexact projections computed by Dykstra’s alternating projection method and generates interior iterates. The ISPG method is a generalization of the spectral projected gradient method, but can be used when projects are difficult to compute. Numerical results for constrained least-squares rectangular matrix problems are presented.

Reviewer: Berwin A. Turlach (Crawley)

MSC:

65K05	Numerical mathematical programming methods
90C06	Large-scale problems in mathematical programming
90C25	Convex programming

Keywords:

projected gradient; nonmonotone line search; spectral gradient; Dykstra’s algorithm; large-scale convex constrained optimization; convergence; alternating projection method; numerical results; least-squares

Software:

SPG