Solving a nonlinear programming using MATLAB?

Hello, experts, just wondering if MATLAB can solve a non-linear programming efficiently. The decision variable is a vector of N, call it a, a is discrete. Has a linear constraint. The objective is p'a+c'max(a-1,0) is nonlinear form.

Can anybody show an example of code? Thanks.

Is this link helpful: http://www.mathworks.com/help/optim/ug/fmincon.html

Answer 1

[Johan Löfberg]

fmincon is not applicable since you have integrality constraints.

The model can easily be converted to a mixed-integer linear problem (if c is non-negative using a standard epigraph reformulation of the max operator, otherwise using a big-M model of it), for which there are many solvers available for MATLAB

The MATLAB toolbox YALMIP makes the modelling easy. Install a MILP solver for good performance (otherwise it uses its own naive implementation)

   N = 10;
   c = rand(N,1);
   p = randn(N,1);
   a = intvar(N,1);
   solvesdp([-5 <= a <= 5],p'*a+c'*max(a-1,0))
   double(a)

Note though, I think you can solve this problem analytically.

[C Zeng]

Thanks, Johan. Yes, I could transfer it to MILP, and solve it.

Is this toolbox free? Let me find it out.

[Johan Löfberg]

yes, just google.

[Matt J]

MATLAB's Optimization Toolbox can solve mixed integer linear programs as of R2014. See intlinprog.