Robust dynamic programming (robust DP) mitigates the effects of ambiguity in transition probabilities on the solutions of Markov decision problems. We consider the computation of robust DP solutions for discrete-stage, infinite-horizon, discounted problems with finite state and action spaces. We present robust modified policy iteration (RMPI) and demonstrate its convergence. RMPI encompasses bo...

We consider a class of inverse problems defined by a nonlinear mapping from parameter or model functions to the data, where the inverse mapping is Hölder continuous with respect to appropriate Banach spaces. We analyze a nonlinear Landweber iteration and prove local convergence and convergence rates with respect to an appropriate distance measure. Opposed to the standard analysis of the nonline...

We discuss in this paper the numerical approximation of fluid-structure interaction (FSI) problems dealing with strong added-mass effect. We propose new semi-implicit algorithms based on inexact block-LU factorization of the linear system obtained after the space-time discretization and linearization of the FSI problem. As a result, the fluid velocity is computed separately from the coupled pre...

Most existing methods for calculating the steady state solution of the lattice Boltzmann equations are based on pseudo time stepping, which often requires a large number of time steps especially for high Reynolds number problems. To calculate the steady state solution directly without the time integration, in this paper we propose and study a nonlinearly preconditioned inexact Newton algorithm ...

A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlappin...

In this paper, we propose a smoothing inexact Newton method for solving variational inequalities with nonlinear constraints. Based on the smoothed Fischer-Burmeister function, the variational inequality problem is reformulated as a system of parameterized smooth equations. The corresponding linear system of each iteration is solved approximately. Under some mild conditions, we establish the glo...

We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through ...

The classical inexact Newton algorithm is an efficient and popular technique for solving large sparse nonlinear system of equations. When the nonlinearities in the system are wellbalanced, a near quadratic convergence is often observed, however, if some of the equations are much more nonlinear than the others in the system, the convergence is much slower. The slow convergence (or sometimes dive...

In this paper we consider a class of convex conic programming. In particular, we propose an inexact augmented Lagrangian (I-AL) method for solving this problem, in which the augmented Lagrangian subproblems are solved approximately by a variant of Nesterov’s optimal first-order method. We show that the total number of first-order iterations of the proposed I-AL method for computing an ǫ-KKT sol...