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We explore how randomization can help asymptotic convergence properties of simple directional search-based optimization methods. Specifically, we develop a cheap, iterative randomized Hessian estimation scheme. We then apply this technique and analyze how it enhances a random directional search method. Then, we proceed to develop a conjugate-directional search method that incorporates estimated Hessian information without requiring the direct use of gradients.doi:10.1080/02331930903100141 fatcat:oigkmtjhtnep3h6rymnah4ljay