In this paper we run two important methods for solving some well-known problems and make a comparison on their performance and efficiency in solving nonlinear systems of equations‎. ‎One of these methods is a non-monotone adaptive trust region strategy and another one is a scaled trust region approach‎. ‎Each of methods showed fast convergence in special problems and slow convergence in other o...

This paper studies the smoothness and curvature of a marginal function for a trust-region problem. In this problem, a quadratic function is minimized over an ellipsoid. The marginal function considered is obtained by perturbing the trust radius, i.e., by changing the size of the ellipsoidal constraint. The values of the marginal function and of its rst and second derivatives are explicitly calc...

An attempt is made to interpret the various existing experimental data on the single spin asymmetries in inclusive pion production by the polarized proton and antiproton beams. As the basis of analysis the chromo-magnetic string model is used. A whole measured kinematic region is covered. The successes and fails of such approach are outlined. The possible improvements of model are discussed.

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks...