Convergence of a projected gradient method variant for quasiconvex objectives

We present a version of the projected gradient method for solving constrained minimization problems with a competitive search strategy: an appropriate step size rule through an Armijo search along the feasible direction, thereby obtaining global convergence properties when the objective function is quasiconvex or pseudoconvex. In contrast to other similar step size rules, this one requires only one projection onto the feasible set per iteration, rather than one projection for each tentative step during the search for the step size, which represents a considerable saving when the projections are computationally expensive.