We seek to find the robust policy that maximizes the expected cumulative reward for the worst case when a partially observable Markov decision process (POMDP) has uncertain parameters whose values are only known to be in a given region. We prove that the robust value function, which represents the expected cumulative reward that can be obtained with the robust policy, is convex with respect to ...

The Mizuno-Todd-Ye predictor-corrector algorithm for linear programming is extended for solving monotone linear complementarity problems from infeasible starting points. The proposed algorithm requires two matrix factorizations and at most three backsolves per iteration. Its computational complexity depends on the quality of the starting point. If the starting points are large enough, then the ...

We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations X + A∗X−1A = Q and X − A∗X−1A = Q, where Q is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton’s method and inversion free variants of the basic fixed point iteration are discussed in some detail for the...

In this paper, a new weighted short-step primal-dual interior point algorithm for convex quadratic optimization (CQO) problems is presented. The algorithm uses at each interior point iteration only full-Newton steps and the strategy of the central path to obtain an ε-approximate solution of CQO. This algorithm yields the best currently wellknown theoretical iteration bound, namely, O( √ n log ε...

Let X, ‖ · ‖ be a Banach space and T a self-map of X. Let xn 1 f T, xn be some iteration procedure. Suppose that F T , the fixed point set of T , is nonempty and that xn converges to a point q ∈ F T . Let {yn} ⊆ X and define n ‖yn 1 − f T, yn ‖. If lim n 0 implies that limyn q, then the iteration procedure xn 1 f T, xn is said to be T -stable. Without loss of generality, we may assume that {yn}...

Abstract Motivated by Pryce’s structural index reduction method for differential algebraic equations (DAEs), we give a complete theoretical analysis about existence and uniqueness of the optimal solution of index reduction problem, and then show the termination and complexity of the fixed-point iteration algorithm. Based on block upper triangular structure of system, we propose the block fixed-...

In this paper, we develop an efficient homogeneous and self-dual interior-point method for the linear programs arising in economic model predictive control. To exploit structure in the optimization problems, the algorithm employs a highly specialized Riccati iteration procedure. Simulations show that in comparison to conventional interior-point methods, our solver is a) significantly faster per...

Stationary One Point Iteration Algorithm of Arbitrary Order of Convergence for Solving the Distance Equation M. A. Sharaf Department of Astronomy, Faculty of Science, King Abdul Aziz University ,Jeddah, Saudi Arabia Abstract. In the present paper, stationary one point iteration algorithm of arbitrary order convergence for solving transcendental equations was given and applied with quintic orde...

We describe a point-based approximate value iteration algorithm for partially observable Markov decision processes. The algorithm performs value function updates ensuring that in each iteration the new value function is an upper bound to the previous value function, as estimated on a sampled set of belief points. A randomized belief-point selection scheme allows for fast update steps. Results i...

Abstract. The purpose of this paper is to address the multiple split common fixed point problem. We present two different methods to approximate a solution of the problem. One is cyclic iteration method; the other is simultaneous iteration method. Under appropriate assumptions on the operators and iterative parameters, we prove both the proposed algorithms converge to the solution of the multip...