In this paper, a modified Hermitian and skew-Hermitian splitting (MHSS) iteration method for solving the complex linear matrix equation AXB = C has been presented. As the theoretical analysis shows, the MHSS iteration method will converge under certain conditions. Each iteration in this method requires the solution of four linear matrix equations with real symmetric positive definite coefficien...

The multiple traveling salesman problem (MTSP) involves scheduling m > 1 salesmen to visit a set of n > m nodes so that each node is visited exactly once. The objective is to minimize the total distance traveled by all the salesmen. The MTSP is an example of combinatorial optimization problems, and has a multiplicity of applications, mostly in the areas of routing and scheduling. In this paper,...

Inspired by the very recent work by Noor and Noor [9] and given a closed convex set-valued mapping C, we propose a split algorithm for solving the problem of finding an element x∗ which is a zero of a given maximal monotone operator T such that its image, Ax∗, under a linear operator, A, is in a closed convex set C(x∗). Then, we present two strong convergence results and state some examples as ...

In the recent paper [M. A. Noor, W. A. Khan, K. I. Noor and Eisa Al-Said, Higher-order iterative methods free from second derivative for solving nonlinear equations, International Journal of the Physical Sciences, Vol. 6 (8) (2011), 1887-1893] several iterative methods for solving nonlinear equations are presented. One of the methods is the three-step iterative method given in Algorithm (2.10) ...

This note shows that the number of arithmetic operations required by any member of a broad class of optimistic policy iteration algorithms to solve a deterministic discounted dynamic programming problem with three states and four actions may grow arbitrarily. Therefore any such algorithm is not strongly polynomial. In particular, the modified policy iteration and λ-policy iteration algorithms a...

In this paper, we consider a very useful and significant class of convex sets and convex functions that is relative convex sets and relative convex functions which was introduced and studied by Noor [20]. Several new inequalities of Hermite-Hadamard type for relative convex functions are established using different approaches. We also introduce relative h-convex functions and is shown that rela...