cauchy.f File Reference

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Functions/Subroutines
subroutine	cauchy (n, x, l, u, nbd, g, iorder, iwhere, t, d, xcp, m, wy, ws, sy, wt, theta, col, head, p, c, wbp, v, nseg, iprint, sbgnrm, info, epsmch)
	Compute the Generalized Cauchy Point along the projected gradient direction. More...

Function/Subroutine Documentation

cauchy()

subroutine cauchy	(	integer	n,
		double precision, dimension(n)	x,
		double precision, dimension(n)	l,
		double precision, dimension(n)	u,
		integer, dimension(n)	nbd,
		double precision, dimension(n)	g,
		integer, dimension(n)	iorder,
		integer, dimension(n)	iwhere,
		double precision, dimension(n)	t,
		double precision, dimension(n)	d,
		double precision, dimension(n)	xcp,
		integer	m,
		double precision, dimension(n, col)	wy,
		double precision, dimension(n, col)	ws,
		double precision, dimension(m, m)	sy,
		double precision, dimension(m, m)	wt,
		double precision	theta,
		integer	col,
		integer	head,
		double precision, dimension(2*m)	p,
		double precision, dimension(2*m)	c,
		double precision, dimension(2*m)	wbp,
		double precision, dimension(2*m)	v,
		integer	nseg,
		integer	iprint,
		double precision	sbgnrm,
		integer	info,
		double precision	epsmch
	)

For given x, l, u, g (with sbgnrm > 0), and a limited memory BFGS matrix B defined in terms of matrices WY, WS, WT, and scalars head, col, and theta, this subroutine computes the generalized Cauchy point (GCP), defined as the first local minimizer of the quadratic

       Q(x + s) = g's + 1/2 s'Bs

along the projected gradient direction P(x-tg,l,u). The routine returns the GCP in xcp.

Parameters

n	On entry n is the dimension of the problem. On exit n is unchanged.
x	On entry x is the starting point for the GCP computation. On exit x is unchanged.
l	On entry l is the lower bound of x. On exit l is unchanged.
u	On entry u is the upper bound of x. On exit u is unchanged.
nbd	On entry nbd represents the type of bounds imposed on the variables, and must be specified as follows: nbd(i)= 0 if x(i) is unbounded, 1 if x(i) has only a lower bound, 2 if x(i) has both lower and upper bounds, and 3 if x(i) has only an upper bound. On exit nbd is unchanged.
g	On entry g is the gradient of f(x). g must be a nonzero vector. On exit g is unchanged.
iorder	iorder will be used to store the breakpoints in the piecewise linear path and free variables encountered. On exit, iorder(1),...,iorder(nleft) are indices of breakpoints which have not been encountered; iorder(nleft+1),...,iorder(nbreak) are indices of encountered breakpoints; and iorder(nfree),...,iorder(n) are indices of variables which have no bound constraits along the search direction.
iwhere	On entry iwhere indicates only the permanently fixed (iwhere=3) or free (iwhere= -1) components of x. On exit iwhere records the status of the current x variables. iwhere(i)= -3 if x(i) is free and has bounds, but is not moved 0 if x(i) is free and has bounds, and is moved 1 if x(i) is fixed at l(i), and l(i) .ne. u(i) 2 if x(i) is fixed at u(i), and u(i) .ne. l(i) 3 if x(i) is always fixed, i.e., u(i)=x(i)=l(i) -1 if x(i) is always free, i.e., it has no bounds.
t	working array; will be used to store the break points.
d	the Cauchy direction P(x-tg)-x
xcp	returns the GCP on exit
m	On entry m is the maximum number of variable metric corrections used to define the limited memory matrix. On exit m is unchanged.
ws	On entry this stores S, a set of s-vectors, that defines the limited memory BFGS matrix. On exit this array is unchanged.
wy	On entry this stores Y, a set of y-vectors, that defines the limited memory BFGS matrix. On exit this array is unchanged.
sy	On entry this stores S'Y, that defines the limited memory BFGS matrix. On exit this array is unchanged.
wt	On entry this stores the Cholesky factorization of (theta*S'S+LD^(-1)L'), that defines the limited memory BFGS matrix. On exit this array is unchanged.
theta	On entry theta is the scaling factor specifying B_0 = theta I. On exit theta is unchanged.
col	On entry col is the actual number of variable metric corrections stored so far. On exit col is unchanged.
head	On entry head is the location of the first s-vector (or y-vector) in S (or Y). On exit col is unchanged.
p	will be used to store the vector p = W^(T)d.
c	will be used to store the vector c = W^(T)(xcp-x).
wbp	will be used to store the row of W corresponding to a breakpoint.
v	working array
nseg	On exit nseg records the number of quadratic segments explored in searching for the GCP.
iprint	variable that must be set by the user. It controls the frequency and type of output generated: iprint<0 no output is generated; iprint=0 print only one line at the last iteration; 0<iprint<99 print also f and |proj g| every iprint iterations; iprint=99 print details of every iteration except n-vectors; iprint=100 print also the changes of active set and final x; iprint>100 print details of every iteration including x and g; When iprint > 0, the file iterate.dat will be created to summarize the iteration.
sbgnrm	On entry sbgnrm is the norm of the projected gradient at x. On exit sbgnrm is unchanged.
info	On entry info is 0. On exit info = 0 for normal return, = nonzero for abnormal return when the the system used in routine bmv is singular.
epsmch	machine precision epsilon

Definition at line 130 of file cauchy.f.

References bmv(), and hpsolb().

Referenced by mainlb().

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