I'm afraid I don't have any ideas. I suppose that would be a question for the Matlab forums.
-- Ray Zimmerman Senior Research Associate 211 Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On Mar 31, 2011, at 9:00 PM, m d wrote: > 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 Zimmerman > Senior Research Associate > 211 Warren Hall, Cornell University, Ithaca, NY 14853 > phone: (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 >
