Non linear optimization using 'optimization toolbox

2015 7 16
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更新时间：2015 7 24
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For the nonlinear optimization problem attached here, how to check, if the function is smooth or not and is it medium scale or large scale problem. Should I use 'fmincon' solver as there is one linear constraint and bounds on the variables?

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Titus Edelhofer
Titus Edelhofer 2015-7-16
Hi,
there is no problem attached? But from your description fmincon should indeed be the correct starting point ...
Titus
learner
learner 2015-7-16
Thanks, Titus. I've attached again. Please tell me how to check 'convexity', 'smoothness' and 'scale' of the problem. Can MATLAB do that?

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Alan Weiss
Alan Weiss 2015-7-16

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The problem is smooth: your objective function is rational. Yes, as the Optimization Decision Table shows, for your problem fmincon is the solver of choice.
Alan Weiss
MATLAB mathematical toolbox documentation

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learner
learner 2015-7-16
Thanks Alan! But please let me know how can I check smoothness of any function. It would be a great help. 'objective function is rational', so every rational function will be smooth? what about non-polynomial (transcendental) functions, are they always non-smooth? Please also let me know 'scale' in layman's words. I've already read mathworks documentation.
Thanks again ...
Brendan Hamm
Brendan Hamm 2015-7-16
Smooth = Continuously Differentiable (twice is sufficient as many algorithms compute the Hessian Matrix)
Large Scale = Minimal Linear Algebra in problem (think sparse matrix operations)
Medium Scale = Lots of Linear Algebra (dense matrix operations)
learner
learner 2015-7-24
Thanks Hamm, Is there any way to check for smoothness quickly in MATLAB like the convex-checker below, which helps a lot for complex functions. http://de.mathworks.com/matlabcentral/fileexchange/23106-convexchecker/content/convexchecker.m

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