optimization algorithms
in [Matlab]
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From: Manthos Vogiatzoglou on 19 Feb 2010 13:50 I optimize a function (log likelihood) with interior point and active set algorithms. I observed a very strange behaviour today. For exactly the same initial values, options and of course function, the two algorithms gave totally different results in iter number zero. Lets assume that the initial values are x0. If I pass x0 to the function (LL) I get a value LL(x0) = v. When I try to optimize LL, the active set algorithm gives the "correct" value of LL(x0) in iteration zero however interior point gives a very different value, than v. This problem appears only for a specific data set and specific constant parameter values. Could this be a bug in interior point algorithm or am I missing something? thanks in advance
From: Matt J on 19 Feb 2010 14:24 "Manthos Vogiatzoglou" <vogia.m(a)gmail.com> wrote in message <hlmmhd$lk2$1(a)fred.mathworks.com>... > I optimize a function (log likelihood) with interior point and active set algorithms. I observed a very strange behaviour today. For exactly the same initial values, options and of course function, the two algorithms gave totally different results in iter number zero. > > Lets assume that the initial values are x0. If I pass x0 to the function (LL) I get a value LL(x0) = v. When I try to optimize LL, the active set algorithm gives the "correct" value of LL(x0) in iteration zero however interior point gives a very different value, than v. > > This problem appears only for a specific data set and specific constant parameter values. Could this be a bug in interior point algorithm or am I missing something? ============= Is x0 the global optimum? And if so, is it the only optimal point? Otherwise, why should the 2 algorithms be expected to return LL(x0)?
From: Manthos Vogiatzoglou on 19 Feb 2010 14:54 I think I better rephase. I know that the value of the function LL, at zero iteration, is LL(x0), where x0 are the initial values. I expect the same result only in ineration zero, because x0 is the same for both algorithms. To put it more... mathematically: I know that: LL(x0) = v active set returns: function value = v at iteration zero interior point returns: function value = b very different than v, again at iteration zero
From: Matt J on 19 Feb 2010 16:15 "Manthos Vogiatzoglou" <vogia.m(a)gmail.com> wrote in message <hlmq8s$mve$1(a)fred.mathworks.com>... > I know that: LL(x0) = v > > active set returns: function value = v at iteration zero > > interior point returns: function value = b very different than v, again at iteration zero ============= I don't have the optimization toolbox, but are you sure that iteration zero is the first function value reported, and not iteration 1? If you were really seeing iteration 1, it could just mean the active set method makes no noticeable initial progress.
From: Kirill on 20 Feb 2010 08:47
On Feb 19, 2:54 pm, "Manthos Vogiatzoglou" <vogi...(a)gmail.com> wrote: > I think I better rephase. > > I know that the value of the function LL, at zero iteration, is LL(x0), where x0 are the initial values. I expect the same result only in ineration zero, because x0 is the same for both algorithms. To put it more... mathematically: > > I know that: LL(x0) = v > > active set returns: function value = v at iteration zero > > interior point returns: function value = b very different than v, again at iteration zero For constrained optimization x0 could be modified to be within the pre- defined bounds? It should be easy to check inside the likelihood function if the passed parameter vector is indeed the same in both cases, in the debugger. Kirill |