how can I do linear programming with a piecewise objective function?
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hello
I have done a linear programming code.And now the objective function of the problem will become a piece-wise function, but still linear in every part of the function.Also, all the constrains are linear as well.
which order can I use to solve the optimizing problem? still the linprog? if yes, how to write the objective function,AKA f. If not, which order can I turn to?
I have tried the fmincon order, but the example in help seems wrong, because I errors happened when I was trying to run it. Is also seems that the description of 'medium-scale programming' in help of linprog suits my requirements, but I cannot figure out how to right the objective function.
thanks
zech
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Alan Weiss
le 22 Fév 2013
Optimization Toolbox solvers generally assume that objective functions are smooth, meaning twice differentiable. They can have difficulty with nonsmooth functions.
That said, there should be no errors even with nonsmooth objectives. If you show us some code we might be able to help diagnose what is going on with your objective or constraint functions.
linprog is unsuitable because it does not handle piecewise-defined objectives and constraints.
It is possible that patternsearch, in Global Optimization Toolbox, is most suitable, because it does not care about smoothness.
Alan Weiss
MATLAB mathematical toolbox documentation
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Alan Weiss
le 27 Fév 2013
Sorry, you found a typo in the documentation. I'll fix that. The syntax is supposed to be
x = fminimax(fun,x0,A,b,Aeq,beq,lb,ub)
Alan Weiss
MATLAB mathematical toolbox documentation
Matt J
le 27 Fév 2013
If your problem size isn't too large (you say it's "medium scale"), you could try a brute force approach. Since your feasible set consists of polygonal pieces, you could find try to find the vertices of all the polygons using
The piecewise linear objective has to be optimized at one of the vertices, so you could just search the values at all vertices to find the optimum.
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