Abstract
The main results reported in this paper are two theorems concerning the use of a newtype of risk-averting error criterion for data fitting. The first states that the convexity region of the risk-averting error criterion expands monotonically as its risk-sensitivity index increases. The risk-averting error criterion is easily seen to converge to the mean squared error criterion as its risk-sensitivity index goes to zero. Therefore, the risk-averting error criterion can be used to convexify the mean squared error criterion to avoid local minima. The second main theorem shows that as the risk-sensitivity index increases to infinity, the risk-averting error criterion approaches the minimax error criterion, which is widely used for robustifying system controllers and filters.
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This material is based upon work supported in part by the National Science Foundation and Army Research Office, but does not necessarily reflect the position or policy of the Government.
An erratum to this article can be found at http://dx.doi.org/10.1007/s10898-009-9421-3
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Lo, J.TH. Convexification for data fitting. J Glob Optim 46, 307–315 (2010). https://doi.org/10.1007/s10898-009-9417-z
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DOI: https://doi.org/10.1007/s10898-009-9417-z
Keywords
- Convexification
- Global optimization
- Local minima
- Data fitting
- Neural network
- Nonlinear regression
- Minimax
- Robustifying error crition
- Degree of robustness