kktchk | R Documentation |

Provide a check on Kuhn-Karush-Tucker conditions based on quantities already computed. Some of these used only for reporting.

kktchk(par, fn, gr, hess=NULL, upper=NULL, lower=NULL, maximize=FALSE, control=list(), ...)

`par` |
A vector of values for the parameters which are supposedly optimal. |

`fn` |
The objective function |

`gr` |
The gradient function |

`hess` |
The Hessian function |

`upper` |
Upper bounds on the parameters |

`lower` |
Lower bounds on the parameters |

`maximize` |
Logical TRUE if function is being maximized. Default FALSE. |

`control` |
A list of controls for the function |

`...` |
The dot arguments needed for evaluating the function and gradient and hessian |

kktchk computes the gradient and Hessian measures for BOTH unconstrained and bounds (and masks) constrained parameters, but the kkt measures are evaluated only for the constrained case.

The output is a list consisting of

`gmax` |
The absolute value of the largest gradient component in magnitude. |

`evratio` |
The ratio of the smallest to largest Hessian eigenvalue. Note that this may be negative. |

`kkt1` |
A logical value that is TRUE if we consider the first (i.e., gradient) KKT condition to be satisfied. WARNING: The decision is dependent on tolerances and scaling that may be inappropriate for some problems. |

`kkt2` |
A logical value that is TRUE if we consider the second (i.e., positive definite Hessian) KKT condition to be satisfied. WARNING: The decision is dependent on tolerances and scaling that may be inappropriate for some problems. |

`hev` |
The calculated hessian eigenvalues, sorted largest to smallest?? |

`ngatend` |
The computed (unconstrained) gradient at the solution parameters. |

`nnatend` |
The computed (unconstrained) hessian at the solution parameters. |

`optim`

cat("Show how kktc works\n") # require(optimx) jones<-function(xx){ x<-xx[1] y<-xx[2] ff<-sin(x*x/2 - y*y/4)*cos(2*x-exp(y)) ff<- -ff } jonesg <- function(xx) { x<-xx[1] y<-xx[2] gx <- cos(x * x/2 - y * y/4) * ((x + x)/2) * cos(2 * x - exp(y)) - sin(x * x/2 - y * y/4) * (sin(2 * x - exp(y)) * 2) gy <- sin(x * x/2 - y * y/4) * (sin(2 * x - exp(y)) * exp(y)) - cos(x * x/2 - y * y/4) * ((y + y)/4) * cos(2 * x - exp(y)) gg <- - c(gx, gy) } ans <- list() # to ensure structure available # If optimx package available, the following can be run. # xx<-0.5*c(pi,pi) # ans <- optimr(xx, jones, jonesg, method="Rvmmin") # ans ans$par <- c(3.154083, -3.689620) kkans <- kktchk(ans$par, jones, jonesg) kkans

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