Gradient Approximation and Multivariable Derivative-Free Optimization Based on Noncommutative Maps
IEEE Transactions on Automatic Control, vol. 67, pp. 6381–6396
Abstract
In this article, multivariable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multivariable objective functions based on noncommutative maps is introduced. The procedure is based on the construction of an exploration sequence to specify where the objective function is evaluated and the definition of so-called gradient generating functions which are composed with the objective function, such that the procedure mimics a gradient descent algorithm. Various theoretical properties of the proposed class of algorithms are investigated and numerical examples are presented.
Authors 3
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Affiliation as printed
Institute for Systems and Control Theory, University of Stuttgart, Berlin, Germany
Univ. of Stuttgart#TAB#
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University of Illinois Urbana-Champaign
Affiliation as printed
ECE, University of Illinois at Urbana-Champaign, Urbana, IL, USA
***University of Illinois at Urbana-Champaign
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Affiliation as printed
Chair of Intelligent Control Systems, RWTH Aachen University, Aachen, Germany
RWTH Aachen University
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