Square root in objective function must appear as nonlinear constraints for optimization?

3 次查看（过去 30 天）
Frank
Frank 2019-3-6
评论： Pedro Luis Camuñas 2020-8-5
The title already described my question. Let me give a specific example:
If I have in my objective function for fmincon to optimize. During the iterations, may be smaller than 0.
Therefore, do I need to write as nonlinear constraints or does Matlab already take account of the problem?
Thank you very much!

请先登录，再回答此问题。

回答（4 个）

Matt J
Matt J 2019-3-6
编辑：Matt J 2019-3-6
You should omit square roots, because they introduce both unneccesary additional computation and non-differentiability into the cost function, which breaks the theoretical assumptions of fmincon. In your example, the problem could be equivalently posed without square roots as
min x^2
s.t. x^2>=100
  6 个评论
显示 4更早的评论
Matt J
Matt J 2019-3-6
编辑：Matt J 2019-3-6
Lastly, Matt, could you please kindly tell me what is the non-differentiability issue? I can differentiate my objective function and nonlinear constraints easily.
The function sqrt(z) has no derivative at z=0. In your case, the function f and hence also t(f) is non-differentiable wherever -x^3+2*x+99=0. So, if the optimal solution lies near such a point, fmincon will not be able to use gradients to find its way there.
What is |t(f)-data|? Is it a least squares objective or is it the L1 norm error between t(f) and |data|? The L1 norm also has differentiability issues.

请先登录，再进行评论。

Matt J
Matt J 2019-3-7
编辑：Matt J 2019-3-7
One general way to get rid of sqrt expressions in the objective is to replace them with an additional nonlinearly constrained variable, e.g., instead of
f=a+b^2+sqrt(-x^3+2*x+99)
have instead,
f=a+b^2+c
s.t. c^2=-x^3+2*x+99
c>=0;
All of the above expressions, both in the objective and the constraints, are now differentiable everywhere.
SandeepKumar R
SandeepKumar R 2019-3-6
Yes, you need to specify that constraint as ignoring this will lead infeasibilty. This is true for any optimizer
Walter Roberson
Walter Roberson 2019-3-6
if you have fractional power of a polynomial (not a multinomial) then manually solve for the bounds and express them as bounds constraints . Bounds constraints are respected in most situations .
You might end up with discontinuous ranges. If so it can often be more efficient to run the ranges as separate problems and take the best solution afterwards . Nonlinear constraints are much less efficient to deal with .

类别

在 Help Center 和 File Exchange 中查找有关 Get Started with Optimization Toolbox 的更多信息

标签

产品


版本

R2014b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by