Browsing by Author "Trosset, Michael"

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    Computing Distances Between Convex Sets and Subsets of the Positive Semidefinite Matrices
    (1997-03) Trosset, Michael
    We describe an important class of semidefinite programming problems that has received scant attention in the optimization community. These problems are derived from considerations in distance geometry and multidimensional scaling and therefore arise in a variety of disciplines, e.g. computational chemistry and psychometrics. In most applications, the feasible positive semidefinite matrices are restricted in rank, so that recent interior-point methods for semidefinite programming do not apply. We establish some theory for these problems and discuss what remains to be accomplished.
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    Numerical Optimization Using Computer Experiments
    (1997-03) Trosset, Michael; Torczon, Virginia
    Engineering design optimization often gives rise to problems in which expensive objective functions are minimized by derivative-free methods. We propose a method for solving such problems that synthesizes ideas from the numerical optimization and computer experiment literatures. Our approach relies on kriging known function values to construct a sequence of surrogate models of the objective function that are used to guide a grid search for a minimizer. Results from numerical experiments on a standard test problem are presented.