donlp2: Solve constrained nonlinear minimization problem

In Rdonlp2: An R extension library to use Peter Spelluci's DONLP2 from R.

Description

Solve constrained nonlinear minimization problem

Usage

donlp2( 
    par, fn,
    par.upper = rep(+Inf, length(par)), par.lower = rep(-Inf, length(par)),   
    A = NULL,
    lin.upper = rep(+Inf, length(par)), lin.lower = rep(-Inf, length(par)), 
    nlin = list(),
    nlin.upper = rep(+Inf, length(nlin)), nlin.lower = rep(-Inf, length(nlin)),
    control = donlp2Control(),
    control.fun = function(lst){return(TRUE)},
    env = .GlobalEnv, 
    name = NULL)

Arguments

fn	the objective function to be minimized. Currently, fn must take only one argument, and the parameter vector(par) will be passed to fn during the optimization. The first element of return value must be the evaluated value. Newly (as of 05/10/2012), fn can be either an R function or an external pointer to a function implemented in, e.g., C (this can speed up the computation considerably). The external pointer mechanism is illustrated by an example in the file wright4ExampleCompiledEval.R, which is in the inst/doc folder of the package.
par	parameter vector(vector object).
par.lower, par.upper	upper and lower bounds for parameter vector, respectively. Their length must equal to length(par). If some elements are unbounded, specify +Inf or -Inf explicitly.
A	the matrix object that represents linear constraints. Its columns must be equal to length(par), and its rows must be equal to the number of linear constraints.
lin.lower, lin.upper	upper and lower bounds for linear constraints, respectively. Their length must equal to the number of linear constraints. If some elements are unbounded, specify +Inf or -Inf explicitly.
nlin	list object whose elements are functions that represents nonlinear constraints. Rule for argument and return value is the same as fn, i.e., these functions take only one arugument(par), and return a vector object whose first element is the evaluated value.
nlin.lower, nlin.upper	upper and lower bounds for nonlinear constraints, respectively. Their length must equal to length(nlin). If some elements are unbounded, specify +Inf or -Inf explicitly.
control	"control parameters" that defines the behavior of Rdonlp2. See donlp2Control for details.
control.fun	donlp2() reports a group of optimization parameters in every iteration(see below for details). This (read-only) information can be available within control.fun(), in which user can decide whether the optimization should be iterrupted. Set its return value to FALSE to interrupt donlp2().
env	the environment in which objective, constraint, control functions are evaluated.
name	an character object that specify file name(without extension, max 40 characters) of output file. If not NULL, DONLP2 creates 2 files(name.pro and name.mes) in current working directory which contain detailed information during the optimization. The amount of information depends te0,te1,te2,te3 specified in donlp2Control.

Value

For n=length(par) parameters, lin linear constraints, and nlin nonlinear constraints, a list with following elements:

par	parameters returned by DONLP2.
gradf	gradient evaluated at par.
u	2*(n+lin+nlin) vector of lagrange multipliers for constraints.
w	2*(n+lin+nlin) vector of penalty term.
step.nr	total number of iterations.
fx	the value of objective function fn.
sci	scaling of fn.
psi	psi the weighted penalty term.
upsi	the unweighted penalty term(L1 norm of constraint vector).
del.k.1	bound for the last active constraints.
b2n0	weighted L2 norm of projected gradients.
b2n	L2norm of gradients based on del.k.1.
nr	number of binding constraints.
sing	value other than -1 indicates working set is singular.
umin	infinity norm of negative part of inequalities multipliers.
not.used	always 0(currently not used)
cond.r	condition number of diagonal part of qr decomposition of normalized gradients of binding constraints
cond.h	condition number of diagonal of cholesky factor of updated full Hessian.
scf0	the relative damping of tangential component if upsi > tau0/2.
xnorm	L2 norm of par.
dnorm	unsclaed norm of d, correction from eqp/qp subproblem.
phase	-1:infeasibility improvement phase, 0: initial optimization, 1:binding constraints unchanged, 2:d small, maratos correction is in use.
c.k	number of decreases of penalty weights.
wmax	infinity norm of weights.
sig.k	stepsize from uidimensional minimization(backgracking).
cfincr	number of objective function evaluations for stepsize algorithm.
dirder	scaled derectional derivative of penalty function along d.
dscal	scaling factor for d.
cosphi	cosine of arc between d and previous d.
violis	number of constraints not binding at current values of par but hit during line search.
hesstype	one of 4 values indicating type of update for Hessian. 1: normal P&M-BFGS update, 0:update suppressed, -1:restart with scaled unit matrix, 2:standard BFGS, 3: BFGS modified by Powell's Device.
modbifgs	modification factor for damping the projector into the BFGS or pantoja-mayne update.
modnr	modification factor for daming the quasi-newton-relation in BFGS.
qpterm	0:if sing==-1, termination indicator of the QP solver, 1:successful, -1:tau becomes larger than tauqp without slack variables becoming sufficiently small.
tauqp	weight of slack variables in QP solver.
infeas	L1 norm of slack variables in QP solver.
nr.update	the approximated newton-raphson update in upper trianglar form.
hessian	numeric Hessian matrix if hessian=TRUE in donlp2Control.
runtime	the elapsed time for the optimization.
message	the termination message.

Author(s)

Peter Spelucci has has written the original solver code, S. Schoeffert has translated donlp2 from f77 to the ANSI C version, K. S. Cove has added dynamic memory allocation, Christoph Bergmeier has added passing objecive and constraints as external pointer, Ryuichi Tamura has written the original Rdonlp2 interface, Diethelm Wuertz has written the current Rdonlp2 interface. DONLP2 is copyrighted software written by Peter Sperucci.

Rdonlp2 documentation built on May 31, 2017, 3:12 a.m.