A trust region affine scaling method for bound constrained optimization (Q1942658)

The author proposes a new trust region affine scaling method for solving bound constrained optimization problems. It combines affine scaling techniques with the trust region strategy. The given method obtains more reduction of the approximate quadratic model from two trial steps, one along some direction defined in an ellipsoid and the other along some newly defined approximate projected gradient. The two trial steps are both located in the standard trust region ball. It is proved that the new method is globally convergent. The author also proves the Q-linear convergence of the objective function values when the second-order sufficient condition holds at a nondegenerate stationary point. The algorithm is tested on some bound constrained optimization problems from CUTEr and compared to LANCELOT and Coleman-Li's algorithm. Preliminary numerical experience verifies the obtained theoretical results.