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...

Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three implementations of approximate MPI (AMPI) that are exten...

We consider the multi-robot task scheduling problem with precedence constraints, and introduce a general algorithm to approximate a solution to this problem. Our algorithm utilizes an iterated auction scheme, in which a batch of tasks that are pairwise unconstrained is selected in each iteration and scheduled using a modified sequential single-item auction. This algorithm also gains flexibility...

The modified iterated Kalman filter, which will be called MIKF for brevity, is derived from the modified Newton method to approximate a maximum likelihood estimate. The MIKF is also obtained by an iteration scheme for the extended Kalman filter equations. A convergence analysis of the MIKF is given. By the damping method, we can reduce the total CPU time needed to estimate the state variables o...

We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are im...

In this paper, we analyze a three-step iterative scheme for three strongly pseudocontractive mappings in a uniformly smooth Banach space. Our results can be viewed as an extension of three-step and two-step iterative schemes of Glowinski and Le Tallec [3], Noor [1215] and Ishikawa [7], Liu [10] and Xu [20]. 2000 Mathematics Subject Classification: Primary 47H10, 47H17: Secondary 54H25

In this paper, we prove the existence of a random common fixed point of two continuous contractive random operators on a separable Banach space. We introduce the random modified Ishikawa iteration scheme and use our existence result to study weak and strong convergence of this scheme to a unique random common fixed point of two random asymptotically quasi-nonexpansive operator. Our work extends...

We analyze in detail two-grid methods for solving the 1D Helmholtz equation discretized by a standard finite-difference scheme. We explain why both basic components, smoothing and coarse-grid correction, fail for high wave numbers, and show how these components can be modified to obtain a convergent iteration. We show how the parameters of a two-step Jacobi method can be chosen to yield a stabl...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...