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Method \code{"L-BFGS-B"} is that of Byrd \emph{et. al.} (1995) which
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Method \code{"L-BFGS-B"} is that of Byrd \emph{et. al.} (1995) which
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allows \emph{box constraints}, that is each variable can be given a lower
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allows \emph{box constraints}, that is each variable can be given a lower
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and/or upper bound. The initial value must satisfy the constraints.
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and/or upper bound. The initial value must satisfy the constraints.
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This uses a limited-memory modification of the BFGS quasi-Newton
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This uses a limited-memory modification of the BFGS quasi-Newton
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method. If non-trivial bounds are supplied, this method will be
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method. If non-trivial bounds are supplied, this method will be
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selected, with a warning.
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selected, with a warning.
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Nocedal and Wright (1999) is a comprehensive reference for the
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Nocedal and Wright (1999) is a comprehensive reference for the
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previous three methods.
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previous three methods.
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{ p <- length(x); sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2) }
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{ p <- length(x); sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2) }
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## 25-dimensional box constrained
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## 25-dimensional box constrained
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optim(rep(3, 25), flb, NULL, method = "L-BFGS-B",
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optim(rep(3, 25), flb, NULL, method = "L-BFGS-B",
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lower = rep(2, 25), upper = rep(4, 25)) # par[24] is *not* at boundary
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lower = rep(2, 25), upper = rep(4, 25)) # par[24] is *not* at boundary
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## "wild" function , global minimum at about -15.81515
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## "wild" function , global minimum at about -15.81515
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fw <- function (x)
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fw <- function (x)
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10*sin(0.3*x)*sin(1.3*x^2) + 0.00001*x^4 + 0.2*x+80
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10*sin(0.3*x)*sin(1.3*x^2) + 0.00001*x^4 + 0.2*x+80
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plot(fw, -50, 50, n = 1000, main = "optim() minimising 'wild function'")
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plot(fw, -50, 50, n = 1000, main = "optim() minimising 'wild function'")
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res <- optim(50, fw, method = "SANN",
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res <- optim(50, fw, method = "SANN",
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control = list(maxit = 20000, temp = 20, parscale = 20))
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control = list(maxit = 20000, temp = 20, parscale = 20))
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res
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res
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## Now improve locally {typically only by a small bit}:
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## Now improve locally {typically only by a small bit}:
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(r2 <- optim(res$par, fw, method = "BFGS"))
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(r2 <- optim(res$par, fw, method = "BFGS"))
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points(r2$par, r2$value, pch = 8, col = "red", cex = 2)
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points(r2$par, r2$value, pch = 8, col = "red", cex = 2)
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## Combinatorial optimization: Traveling salesman problem
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## Combinatorial optimization: Traveling salesman problem
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library(stats) # normally loaded
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library(stats) # normally loaded
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eurodistmat <- as.matrix(eurodist)
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eurodistmat <- as.matrix(eurodist)
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