In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function f (x), obtained from stochastic observations of the function or its gradient. Our method also utilizes estimates of function values to gauge progress that is being made. The convergence analysis relies on requirements that these models and these estimates are sufficiently accurate with high enough, but fixed, probability. Beyond these conditions, no assumptions are made on how these models and estimates are generated. Under these general conditions we show an almost sure global convergence of the method to a first order stationary point. In the second part of the paper, we present examples of generating sufficiently accurate random models under biased or unbiased noise assumptions. Lastly, we present some computational results showing the benefits of the proposed method compared to existing approaches that are based on sample averaging or stochastic gradients.

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We describe an optimization-based method that seeks the superposition of ligand binding cavities that maximizes their overlapping volume. Our method, called DFO-VASP, iteratively uses Boolean set operations to evaluate overlapping volume in intermediate superpositions while searching for the maximal one. Our results verify that the superpositions identified are biologically relevant, and demonstrate that DFO-VASP generally discovers cavity superpositions with similar or occasionally larger overlapping volume than those of superpositions generated with existing means.

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