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ccsaq

Conservative Convex Separable Approximation with Affine Approximation plus Quadratic Penalty


Description

This is a variant of CCSA ("conservative convex separable approximation") which, instead of constructing local MMA approximations, constructs simple quadratic approximations (or rather, affine approximations plus a quadratic penalty term to stay conservative)

Usage

ccsaq(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL,
  hinjac = NULL, nl.info = FALSE, control = list(), ...)

Arguments

x0

starting point for searching the optimum.

fn

objective function that is to be minimized.

gr

gradient of function fn; will be calculated numerically if not specified.

lower, upper

lower and upper bound constraints.

hin

function defining the inequality constraints, that is hin>=0 for all components.

hinjac

Jacobian of function hin; will be calculated numerically if not specified.

nl.info

logical; shall the original NLopt info been shown.

control

list of options, see nl.opts for help.

...

additional arguments passed to the function.

Value

List with components:

par

the optimal solution found so far.

value

the function value corresponding to par.

iter

number of (outer) iterations, see maxeval.

convergence

integer code indicating successful completion (> 1) or a possible error number (< 0).

message

character string produced by NLopt and giving additional information.

Note

“Globally convergent” does not mean that this algorithm converges to the global optimum; it means that it is guaranteed to converge to some local minimum from any feasible starting point.

References

Krister Svanberg, “A class of globally convergent optimization methods based on conservative convex separable approximations,” SIAM J. Optim. 12 (2), p. 555-573 (2002).

See Also

Examples

##  Solve the Hock-Schittkowski problem no. 100 with analytic gradients
x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1)
fn.hs100 <- function(x) {
    (x[1]-10)^2 + 5*(x[2]-12)^2 + x[3]^4 + 3*(x[4]-11)^2 + 10*x[5]^6 +
                  7*x[6]^2 + x[7]^4 - 4*x[6]*x[7] - 10*x[6] - 8*x[7]
}
hin.hs100 <- function(x) {
    h <- numeric(4)
    h[1] <- 127 - 2*x[1]^2 - 3*x[2]^4 - x[3] - 4*x[4]^2 - 5*x[5]
    h[2] <- 282 - 7*x[1] - 3*x[2] - 10*x[3]^2 - x[4] + x[5]
    h[3] <- 196 - 23*x[1] - x[2]^2 - 6*x[6]^2 + 8*x[7]
    h[4] <- -4*x[1]^2 - x[2]^2 + 3*x[1]*x[2] -2*x[3]^2 - 5*x[6]	+11*x[7]
    return(h)
}
gr.hs100 <- function(x) {
   c(  2 * x[1] -  20,
      10 * x[2] - 120,
       4 * x[3]^3,
       6 * x[4] - 66,
      60 * x[5]^5,
      14 * x[6]   - 4 * x[7] - 10,
       4 * x[7]^3 - 4 * x[6] -  8 )}
hinjac.hs100 <- function(x) {
    matrix(c(4*x[1], 12*x[2]^3, 1, 8*x[4], 5, 0, 0,
        7, 3, 20*x[3], 1, -1, 0, 0,
        23, 2*x[2], 0, 0, 0, 12*x[6], -8,
        8*x[1]-3*x[2], 2*x[2]-3*x[1], 4*x[3], 0, 0, 5, -11), 4, 7, byrow=TRUE)
}

# incorrect result with exact jacobian
S <- ccsaq(x0.hs100, fn.hs100, gr = gr.hs100,
            hin = hin.hs100, hinjac = hinjac.hs100,
            nl.info = TRUE, control = list(xtol_rel = 1e-8))


S <- ccsaq(x0.hs100, fn.hs100, hin = hin.hs100,
            nl.info = TRUE, control = list(xtol_rel = 1e-8))

nloptr

R Interface to NLopt

v1.2.2.2
LGPL-3
Authors
Jelmer Ypma [aut, cre], Steven G. Johnson [aut] (author of the NLopt C library), Hans W. Borchers [ctb], Dirk Eddelbuettel [ctb], Brian Ripley [ctb] (build process on multiple OS), Kurt Hornik [ctb] (build process on multiple OS), Julien Chiquet [ctb], Avraham Adler [ctb] (removal deprecated calls from tests, <https://orcid.org/0000-0002-3039-0703>)
Initial release
2020-07-02

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