Thanks a lot for your response and also the reference. I read the algorithm. It hase been said that fmincon uses a quasi-Newton approximation to the Hessian by the BFSG formula, as you mentioned. However, the hessian is the second derivative of the Lagrangian function w.r.t X. So it should be close to the hessian provided by Lxx in mips, since Lxx is the accurate second derivative of Lagrangian function. Can you explaine me why there is such a large difference as follow:
Hessian provided by fmincon = 2.2313 8.7213 8.7213 60.3726 Hessian (Lxx) provided by mips = -0.3666 0 0 -0.0046 Please note that the optimal solution given by both solvers, mips & fmincon, are equal, just different in their supplied hessian. Thanks in advance --- On Wed, 3/30/11, Ray Zimmerman <[email protected]> wrote: From: Ray Zimmerman <[email protected]> Subject: Re: mips & fmincon To: "MATPOWER discussion forum" <[email protected]> Date: Wednesday, March 30, 2011, 4:17 PM Based on the fmincon documentation, fmincon has a number of ways of handling the Hessian, depending on the algorithm. In many cases it uses a quasi-Newton approximation to the Hessian. I suspect that's what you're seeing. -- Ray ZimmermanSenior Research Associate211 Warren Hall, Cornell University, Ithaca, NY 14853phone: (607) 255-9645 On Mar 30, 2011, at 3:46 PM, m d wrote: Hello all, I've faced with an interesting question and appreciate if anyone can answer! When I use "mips" as an optimization solver to solve one of those simple optimization problems with constraint in t-mips.m, I get a hessian of the lagrangian by calling " Lxx" . The hessian provided in Lxx is closely matched with that I compute the problem by hand. However, when I use "fmincon" to solve the same problem as following: [x,fval,exitflag,output,lambda,grad,hessian] = fmincon(...) and compare its hessian with Lxx, I observe a huge diffence, though the optimal answers for x and objective function are the same. Can anyone answer why? What is the algorithm used in fmincon to compute the hessian? Thanks in advance for your reply, Maryam
