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

##### MSC:
 65K05 Mathematical programming (numerical methods) 90C06 Large-scale problems (mathematical programming) 90C25 Convex programming
SPG