title: Matrix function minimzation
body: <p>If I wanted to minimize the function <code>f(x,y)=(abs(x+y)-abs(x)-abs(y))</code> squared, subject to a bunch of linear constraints, where <code>x</code> and <code>y</code> are real vectors or real arrays.</p>
  
  <p>There are two problems:
  - The function is not exactly convex (though certain linear cuts through it are), meaning that algorithms that use differentiation to minimize maybe won't work.
  - The function to minimize does not return a real scalar, and the most common algorithms for maximization (at least in MATLAB with fmincon and fminsearch) require the objective function to return scalars.</p>
  
  <p>Is there a way I can solve this cleanly numerically using whatever technology? </p>