fminbnd got stock in local minimum: can global search deal with the problem defined by cases?

I plot the value of a function over the possible values and also run fminbnd. I find out that fminbud got stuck in a local minimum. As a next step I would consider global optimization toolbox. Can they handle function defined by cases?

Answer 1

[Alan Stevens]

Narrow the allowed search interval. If you've plotted the function you should be able to get a good idea of where the global minimum lies.

[alpedhuez]

Fair. But I have optimization problems with various parameters. Thus one does not want to do it. How about patternsearch for nonsmooth problems?

https://www.mathworks.com/help/gads/global-solver-choices.html#SolverPerformanceWithANonsmoothProblemExample-2

[Alan Stevens]

Perhaps. I've no knowledge of patternsearch so can't really comment. An alternative might be to adopt something like a particle swarm optimisation (PSO) approach, for which there are several routines to be found in the File Exchange.

[alpedhuez]

Working on it.

Answer 2

[Walter Roberson]

fminbnd() cannot handle functions defined by cases. None of the functions in the Optimization toolbox can: they all depend upon the function having continuous first derivatives (an some of them depend upon the function also having continuous second derivatives.)

The optimization functions that can work on functions that are defined by cases are: ga(), gamultiobj(), patternsearch(), particleswarm(), simulannealbnd()