Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms

2011 ◽  
Vol 21 (3) ◽  
pp. 761-781 ◽  
Author(s):  
Stefan M. Wild ◽  
Christine Shoemaker
Keyword(s):  
Global Convergence ◽  
Radial Basis Function ◽  
Basis Function ◽  
Trust Region ◽  
Derivative Free ◽  
Radial Basis

scholarly journals Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

2021 ◽  
Vol 26 (2) ◽  
pp. 31
Author(s):  
Manuel Berkemeier ◽  
Sebastian Peitz
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Optimization Problems ◽  
Trust Region ◽  
Surrogate Models ◽  
Descent Method ◽  
Information Need ◽  
Derivative Free ◽  
Radial Basis ◽  
General Scalar

We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point is proven. The method is derivative-free in the sense that derivative information need not be available for the expensive objectives. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar counterparts and complements multiobjective line-search algorithms. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points needed per iteration scales linearly with the decision space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives.

scholarly journals Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Mohie Mortadha Alqezweeni ◽  
Vladimir Ivanovich Gorbachenko ◽  
Maxim Valerievich Zhukov ◽  
Mustafa Sadeq Jaafar
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Boundary Value ◽  
Trust Region Method ◽  
Trust Region ◽  
Radial Basis Function Networks ◽  
Structure Selection ◽  
Region Method ◽  
Radial Basis

A method using radial basis function networks (RBFNs) to solve boundary value problems of mathematical physics is presented in this paper. The main advantages of mesh-free methods based on RBFN are explained here. To learn RBFNs, the Trust Region Method (TRM) is proposed, which simplifies the process of network structure selection and reduces time expenses to adjust their parameters. Application of the proposed algorithm is illustrated by solving two-dimensional Poisson equation.

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