Non linear optimization using 'optimization toolbox

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?

[Titus Edelhofer]

Hi,

there is no problem attached? But from your description fmincon should indeed be the correct starting point ...

Titus

[learner]

Thanks, Titus. I've attached again. Please tell me how to check 'convexity', 'smoothness' and 'scale' of the problem. Can MATLAB do that?

Answer 1

[Alan Weiss]

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

[learner]

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]

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]

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