title: Alternative to scipy.optimize.minimize constrained optimization?
body: <p>I am interested in finding optimized parameters of a model (by minimizing the model's output with the known value). The parameters I am interested in finding have bounds and they are also constrained by an inequality that looks like <code>1 - sum(x_par) &gt;= 0</code>, where <code>x_par</code> is a list of some of the parameters out of the total parameter list. I have used <a href="http://scipy.optimize.minimize" rel="nofollow noreferrer"><code>scipy.optimize.minimize</code></a> to minimize this problem with different methods (such as <code>COBYLA</code> and <code>SLSQP</code>), but the fitting performance by this function is quite poor and the error is generally above 50%. </p>
  
  <p>I have noticed that <a href="https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.curve_fit.html" rel="nofollow noreferrer"><code>scipy.optimize.curve_fit</code></a> and <a href="https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.differential_evolution.html" rel="nofollow noreferrer"><code>scipy.optimize.differential_evolution</code></a> work very well in terms of fitting the given values, but these functions do not allow constraints on parameters. I am looking for an alternative in python to optimize my problem that allows constraining parameters and can do a better job in fitting the given curve/values than <a href="http://scipy.optimize.minimize" rel="nofollow noreferrer"><code>scipy.optimize.minimize</code></a>.</p>