However, the linear approximations are likely only good approximations near the current simplex, so the linear program is given the further requirement that the solution, which will become x_(j+1), must be within RHO_j from x_j. RHO_j only decreases, never increases. The initial RHO_j is rhobeg and the final RHO_j is rhoend. In this way COBYLA's iterations behave like a trust region algorithm. Additionally, the linear program may be inconsistent, or the approximation may give poor improvement. For details about how these issues are resolved, as well as how the points v_i are updated, refer to the source code or the references below. References ---------- Powell M.J.D. (1994), "A direct search optimization method that models the objective and constraint functions by linear interpolation.", in Advances in Optimization and Numerical Analysis, eds. S. Gomez and J-P Hennart, Kluwer Academic (Dordrecht), pp. 51-67 Powell M.J.D. (1998), "Direct search algorithms for optimization calculations", Acta Numerica 7, 287-336 Powell M.J.D. (2007), "A view of algorithms for optimization without derivatives", Cambridge University Technical Report DAMTP 2007/NA03 Examples -------- Minimize the objective function f(x,y) = x*y subject to the constraints x**2 + y**2 < 1 and y > 0:: >>> def objective(x): ... return x[0]*x[1] ... >>> def constr1(x): ... return 1 - (x[0]**2 + x[1]**2) ... >>> def constr2(x): ... return x[1] ... >>> from scipy.optimize import fmin_cobyla >>> fmin_cobyla(objective, [0.0, 0.1], [constr1, constr2], rhoend=1e-7) array([-0.70710685, 0.70710671]) The exact solution is (-sqrt(2)/2, sqrt(2)/2). zLcons must be a sequence of callable functions or a single callable function.Nc