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A previous analysis of second-order behavior of generalized pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search (MADS) algorithms for general constrained optimization. Because of the ability of MADS to generate an asymptotically dense set of search directions,(More)
The purpose of this paper is to introduce a new way of choosing directions for the Mesh Adaptive Direct Search (MADS) class of algorithms. The advantages of this new ORTHOMADS instantiation of MADS are that the polling directions are chosen deterministically, ensuring that the results of a given run are repeatable, and that they are orthogonal to each(More)
A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specifically this paper concentrates on the GPS poll step. Polling is done to(More)
In previous work, the generalized pattern search (GPS) algorithm for linearly constrained (continuous) optimization was extended to mixed variable problems, in which some of the variables may be categorical. In another paper, the mesh adaptive direct search (MADS) algorithm was introduced as a generalization of GPS for problems with general nonlinear(More)
views expressed in this paper are those of the authors and do not reflect the official policy or position of the Abstract The class of generalized pattern search (GPS) algorithms for mixed variable optimization is extended to problems with stochastic objective functions, by augmenting it with ranking and selection (R&S). Asymptotic convergence for the(More)
In this paper, we characterize a new class of com-putationally expensive optimization problems and introduce an approach for solving them. In this class of problems, objective function values may be directly related to the computational time required to obtain them, so that, as the optimal solution is approached, the computational time required to evaluate(More)
This paper introduces a new approach to the problem of quantitatively reconstructing cylindrically symmetric objects from radiograph data obtained via x-ray tomography. Specifically , a mixed variable programming (MVP) problem is formulated, in which the variables of interest are the number and types of materials and the thickness of each concentric layer.(More)