Convergence properties of projected gradient methods with nonmonotonic back tracking technique for convex constrained optimization (Q2721959)

The paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems. Tie mixed strategy is adopted which swich switches to backtracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature. It is proved that the proposed algorithms are globally convergent and have local superlinear convergent rate under some reasonable conditions. Some illustrative numerical experiments are given.