Convex estimators for optimization of kriging model problems
By: Hamza, Karim
.
Contributor(s): Shalaby, Mohammed.
Publisher: New York ASME 2012Edition: Vol.134(11), Nov.Description: 1-11p.Subject(s): Mechanical EngineeringOnline resources: Click here
In:
Journal of mechanical designSummary: This paper presents a framework for identification of the global optimum of Kriging models that have been tuned to approximate the response of some generic objective function and constraints. The framework is based on a branch and bound scheme for subdivision of the search space into hypercubes while constructing convex underestimators of the Kriging models. The convex underestimators, which are the key development in this paper, provide a relaxation of the original problem. The relaxed problem has two main features: (i) convex optimization algorithms such as sequential quadratic programming (SQP) are guaranteed to find the global optimum of the relaxed problem and (ii) objective value of the relaxed problem is a lower bound within a hypercube for the original (Kriging model) problem. As accuracy of the convex estimators improves with subdivision of a hypercube.
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This paper presents a framework for identification of the global optimum of Kriging models that have been tuned to approximate the response of some generic objective function and constraints. The framework is based on a branch and bound scheme for subdivision of the search space into hypercubes while constructing convex underestimators of the Kriging models. The convex underestimators, which are the key development in this paper, provide a relaxation of the original problem. The relaxed problem has two main features: (i) convex optimization algorithms such as sequential quadratic programming (SQP) are guaranteed to find the global optimum of the relaxed problem and (ii) objective value of the relaxed problem is a lower bound within a hypercube for the original (Kriging model) problem. As accuracy of the convex estimators improves with subdivision of a hypercube.
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