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A gradient projection method with feasible inexact projections is proposed inthe present paper. The inexact projection is performed using a relative errortolerance. Asymptotic convergence analysis and iteration-complexity bounds ofthe method employing constant and Armijo step sizes are presented. Numericalresults are reported illustrating the potential advantages of consideringinexact projections instead of exact ones in some medium scale instances of aleast squares problem over the spectrohedron.

Inexact gradient projection method with relative error tolerance