Random search methods are widely used to solve optimization problems arising from various practical areas. One key characteristic of such methods is that they depend very little on the structures of the underlying problems, which makes them of particular interest to practitioners.;An important question for random search algorithms is how to make them adaptive so that they can effectively exploit information acquired during execution for efficient discovery of optimal solutions. For example, an algorithm can be adaptive in the sense that it adjusts its key parameters dynamically so as to guide the search toward better move, or it strategically concentrates the computational effort on shrinking the promising subset of the feasible region.;In this dissertation we present two adaptive random search algorithms. For the first algorithm, we parameterize a sequential random search method (Improving Hit-and-Run) and select at each iteration the parameter value maximizing a defined measure of improvement given the location of the current iterate. The algorithm is initially developed for a special class of convex problems but it also applies to global optimization of Lipschitz functions. The second algorithm is designed for optimization of noisy functions. It iteratively focuses the computational effort on shrinking subsets of the feasible region resulting from adaptive branching and pruning actions. Some sampling-related parameters are also dynamically chosen to effectively balance the tradeoff between the computational effort spent on estimating the noise contaminated objective function value and that used for exploration of better solutions.;The second algorithm is also applied to two challenging optimization problems that arise from design of experiments and portfolio optimization respectively.
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