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Inexact spectral projected gradient methods on convex sets
Authors:Birgin  Ernesto G; Martinez  Jose Mario; Raydan  Marcos
Institution: 1 Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010 Cidade Universitária, 05508-090 São Paulo, Brazil 2 Departamento de Matemática Aplicada, IMECC-UNICAMP, CP 6065, 13081-970 Campinas SP, Brazil 3 Departamento de Computación, Facultad de Ciencias, Universidad Central de Venezuela, Ap. 47002, Caracas 1041-A, Venezuela
Abstract:A new method is introduced for large-scale convex constrainedoptimization. The general model algorithm involves, at eachiteration, the approximate minimization of a convex quadraticon the feasible set of the original problem and global convergenceis obtained by means of nonmonotone line searches. A specificalgorithm, the Inexact Spectral Projected Gradient method (ISPG),is implemented using inexact projections computed by Dykstra'salternating projection method and generates interior iterates.The ISPG method is a generalization of the Spectral ProjectedGradient method (SPG), but can be used when projections aredifficult to compute. Numerical results for constrained least-squaresrectangular matrix problems are presented.
Keywords:Convex constrained optimization  projected gradient  nonmonotone line search  spectral gradient  Dykstra's algorithm
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