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CONORBIT: constrained optimization by radial basis function interpolation in trust regions. (English) Zbl 1367.65091
Summary: This paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm [S. M. Wild et al., SIAM J. Sci. Comput. 30, No. 6, 3197–3219 (2008; Zbl 1178.65065)]. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, a chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA [M. J. D. Powell, in: Advances in optimization and numerical analysis. Proceedings of the 6th workshop on optimization and numerical analysis, Oaxaca, Mexico, January 1992. Dordrecht: Kluwer Academic Publishers. 51–67 (1994; Zbl 0826.90108)], a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.

MSC:
65K05 Numerical mathematical programming methods
90C51 Interior-point methods
90C52 Methods of reduced gradient type
90C30 Nonlinear programming
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