About use Yalmip to solve nonlinear problem

[Fei Yan]

I'm using Yalmip to solve a nonlinear problem with 500 variables. Both Fmincon and bmibnb solvers do not work. Do you have any solvers recommended to solve nonlinear problems? 

[Johan Löfberg]

http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Category.NonlinearProgrammingSolver

But it is all about the model. A poorly modeled problem will never work even with the best possible solver.

[Fei Yan]

If there is a piece-wise function inside, normally how will you deal with it. For example, max z= x*(1-y)+1 . when x>=1  y=2x-1; x<1, y=x^2.  

[Johan Löfberg]

First, clearly a hard  model as you are maximizing a convex function

Various options

You model it using binary variables and implies, although that will lead to a nasty nonlinear mixed-integer program.

You approcimate it using a pwa function and sos2 operators leading to a MILP

You model it using an anonymous black-box function using sdpfun (no derivatives will be available then)

You define your own overloaded operator and define derivatives etc (i.e,. copy logic in, e.g., sdpvar/atan)