I am using optimx with BFGS method and differ initial points. I have objerved that it converges on points that they are not optima. Does anybody can explain to me how that problem is faced up? Thanks in advance for your time.
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Erwin Kalvelagen
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Christina
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Is the problem convex? – Erwin Kalvelagen Jul 16 '16 at 01:40
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Yes it is. One of the functions I tested was Bohachevsky on 2 dimensions: http://www.sfu.ca/~ssurjano/boha.html. – Christina Jul 17 '16 at 17:03
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Make sure you provide exact and correct gradients. – Erwin Kalvelagen Jul 17 '16 at 17:15
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In the optimx I have written: gr= grad and at the begging of the code I define the grad as following: grad <- function(xx){ x1 <- xx[1] x2 <- xx[2] gg <- as.vector(rep(0, 2)) gg[1] <-2.82743*sin(3*pi*x1) #dif.f.x1 gg[2] <- 5.02655*sin(4*pi*x2) #dif.f.x2 return(gg) } I did the same wth Hessian – Christina Jul 18 '16 at 13:33
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Sorry, these functions are not convex. You need a global solver for this. – Erwin Kalvelagen Jul 18 '16 at 23:39
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Could you please explain what do yoy mean by "global solver" – Christina Jul 19 '16 at 16:47
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A global solver is a solver that does not converge to a local optimum but seeks global optimal solutions, – Erwin Kalvelagen Jul 19 '16 at 17:14
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Ok. Is optimx used only for local optimum? – Christina Jul 19 '16 at 18:08
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I believe the solvers mentioned in the optimx docs are all local solvers, i.e. they converge to a local optimal solution.. – Erwin Kalvelagen Jul 19 '16 at 18:51
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What are you suggested to use instead of optimx? – Christina Jul 19 '16 at 21:08
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There are quite a few good global solvers. E.g. [baron](http://archimedes.cheme.cmu.edu/?q=baron), [couenne](https://projects.coin-or.org/Couenne), [Antigone](http://helios.princeton.edu/ANTIGONE/), and Lindo Global. Some of them you can try out on [NEOS](https://neos-server.org/neos/). Also some of them don't support trig functions. – Erwin Kalvelagen Jul 19 '16 at 22:48