In this paper, we study the problem of searching for a moving object with multiple agents where each agent can access only a subset of a discrete search space at any time. We develop necessary conditions for an optimal search plan, extending prior results in search theory. Using these necessary conditions, we develop a forward-backward algorithm based on coordinate descent techniques to obtain solutions. For the case where agent's probabilities of detection depend only on the cell being searched, each iteration can be reduced to solution of a network optimization problem. To avoid local minima, we derive a convex relaxation of the dynamic search problem and show this can be solved optimally using coordinate descent techniques. The solutions of the relaxed problem are used to provide random starting conditions for the iterative algorithm. We also address the problem where the probabilities of detection depend on agents, time periods and locations. We reduce the problem to a submodular maximization problem over a matroid and give a greedy algorithm with performance guarantees. We illustrate the performance of our algorithms with experiments and compare the results with alternative algorithms based on combinatorial techniques.