Apotentialreductionalgorithmisproposedforoptimizationofaconvexfunctionsubjecttolinearconstraints.Ateachstepofthealgorithm,asystemoflinearequationsissolvedtogetasearchdirectionandtheArmijo'sruleisusedtodetermineastepsize.Itisprovedthatthealgorithmisgloballyconvergent.Computationalresultsarereported.