Is there any way to define a loss function in optimization problems?

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Philipp Glira
Philipp Glira 2021-3-10
编辑： Walter Roberson 2021-3-10
Is there any way to define a loss function when setting up an optimization problem using the optimization toolbox?
Main purpose: outlier detection.
Examples for loss functions in other optimization libraries:

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回答（1 个）

Matt J
Matt J 2021-3-10
Yes, absolutely. Without a function to optimize, it's not an optimization problem.
  2 个评论
Philipp Glira
Philipp Glira 2021-3-10
My questions was regarding loss functions.
The main purpose of a loss function is the detection of outliers. In other words, it makes the optimization robust against gross observation errors (=outliers).
I don't see any possibility in the documentation of the optimization toolbox to define such a loss function, but maybe I have just overlooked that part.
To clarify:
1) non-robust optimization, i.e. without loss function:
(see the 3 outliers with large y values)
2) robust optimization, i.e. with loss function:
(the 3 outliers are detected as outliers and thus have no influence on the estimated unknowns)
Matt J
Matt J 2021-3-10
编辑：Matt J 2021-3-10
No, there are no outlier rejection utilities in the Optimization Toolbox solvers. The Computer Vision Toolbox, however, does have a RANSAC routine,
https://www.mathworks.com/help/vision/ref/ransac.html
You could also try removing outliers with rmoutliers,
https://www.mathworks.com/help/matlab/ref/rmoutliers.html

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