Is there an opensource alternative to MATLAB’s fmincon
function for constrained linear optimization? I’m rewriting a MATLAB program to use Python / NumPy / SciPy and this is the only function I haven’t found an equivalent to. A NumPybased solution would be ideal, but any language will do.
Is your problem convex? Linear? Nonlinear? I agree that SciPy.optimize will probably do the job, but fmincon is a sort of bazooka for solving optimization problems, and you’ll be better off if you can confine it to one of the categories below (in increasing level of difficulty to solve efficiently)
 Linear Program (LP)
 Quadratic Program (QP)
 Convex QuadraticallyConstrained Quadratic Program (QCQP)
 Second Order Cone Program (SOCP)
 Semidefinite Program (SDP)
 NonLinear Convex Problem
 NonConvex Problem
There are also combinatoric problems such as MixedInteger Linear Programs (MILP), but you didn’t mention any sort of integrality constraints, suffice to say that they fall into a different class of problems.
The CVXOpt package will be of great use to you if your problem is convex.
If your problem is not convex, you need to choose between finding a local solution or the global solution. Many convex solvers ‘sort of’ work in a nonconvex domain. Finding a good approximation to the global solution would require some form Simulated Annealing or Genetic Algorithm. Finding the global solution will require an enumeration of all local solutions or a combinatorial strategy such as Branch and Bound.
Python optimization software:

OpenOpt http://openopt.org (this one is numpybased as you wish, with automatic differentiation by FuncDesigner)

Pyomo https://software.sandia.gov/trac/coopr/wiki/Package/pyomo
The open source Python package,SciPy, has quite a large set of optimization routines including some for multivariable problems with constraints (which is what fmincon does I believe). Once you have SciPy installed type the following at the Python command prompt
help(scipy.optimize)
The resulting document is extensive and includes the following which I believe might be of use to you.
Constrained Optimizers (multivariate)
fmin_l_bfgs_b  Zhu, Byrd, and Nocedal's LBFGSB constrained optimizer
(if you use this please quote their papers  see help)
fmin_tnc  Truncated Newton Code originally written by Stephen Nash and
adapted to C by JeanSebastien Roy.
fmin_cobyla  Constrained Optimization BY Linear Approximation
GNU Octave is another MATLAB clone that might have what you need.
For numerical optimization in Python you may take a look at OpenOpt solvers:
I don’t know if it’s in there, but there’s a python distribution called Enthought that might have what you’re looking for. It was designed specifically for data analysis has over 60 additional libraries.
Have a look at http://www.aemdesign.com/downloadfsqp.htm.
There you will find C code which provides the same functionality as fmincon
. (However, using a different algorithm. You can read the manual if you are interested in the details.)
It’s open source but not under GPL.
There is a program called SciLab that is a MATLAB clone.
I haven’t used it at all, but it is open source and might have the function you are looking for.
Octave in the latest version implements an equivalent to the Matlab fmincon function into the optimization package.
Scilab has an implementation of fmincon (using IPOpt) which is now regularly updated:
https://atoms.scilab.org/toolboxes/fmincon
For largescale optimization it outperforms Matlab’s fmincon.