SUBSMRun Method

public void Run(
	int N,
	int M,
	int NSUB,
	int[] IND,
	int offset_ind,
	double[] L,
	int offset_l,
	double[] U,
	int offset_u,
	int[] NBD,
	int offset_nbd,
	ref double[] X,
	int offset_x,
	ref double[] D,
	int offset_d,
	double[] WS,
	int offset_ws,
	double[] WY,
	int offset_wy,
	double THETA,
	int COL,
	int HEAD,
	ref int IWORD,
	ref double[] WV,
	int offset_wv,
	double[] WN,
	int offset_wn,
	int IPRINT,
	ref int INFO
)

Public Sub Run ( 
	N As Integer,
	M As Integer,
	NSUB As Integer,
	IND As Integer(),
	offset_ind As Integer,
	L As Double(),
	offset_l As Integer,
	U As Double(),
	offset_u As Integer,
	NBD As Integer(),
	offset_nbd As Integer,
	ByRef X As Double(),
	offset_x As Integer,
	ByRef D As Double(),
	offset_d As Integer,
	WS As Double(),
	offset_ws As Integer,
	WY As Double(),
	offset_wy As Integer,
	THETA As Double,
	COL As Integer,
	HEAD As Integer,
	ByRef IWORD As Integer,
	ByRef WV As Double(),
	offset_wv As Integer,
	WN As Double(),
	offset_wn As Integer,
	IPRINT As Integer,
	ByRef INFO As Integer
)

Parameters

N  Int32

is an integer variable. On entry n is the dimension of the problem. On exit n is unchanged.

M  Int32

is an integer variable. On entry m is the maximum number of variable metric corrections used to define the limited memory matrix. On exit m is unchanged.

NSUB  Int32

is an integer variable. On entry nsub is the number of free variables. On exit nsub is unchanged.

IND  Int32

is an integer array of dimension nsub. On entry ind specifies the coordinate indices of free variables. On exit ind is unchanged.

offset_ind  Int32

 

L  Double

is a double precision array of dimension n. On entry l is the lower bound of x. On exit l is unchanged.

offset_l  Int32

 

U  Double

is a double precision array of dimension n. On entry u is the upper bound of x. On exit u is unchanged.

offset_u  Int32

 

NBD  Int32

is a integer array of dimension n. 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.

offset_nbd  Int32

 

X  Double

is a double precision array of dimension n. On entry x specifies the Cauchy point xcp. On exit x(i) is the minimizer of Q over the subspace of free variables.

offset_x  Int32

 

D  Double

= -(Z'BZ)^(-1) r. The formula for the Newton direction, given the L-BFGS matrix and the Sherman-Morrison formula, is d = (1/theta)r + (1/theta*2) Z'WK^(-1)W'Z r. where K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] [L_a -R_z theta*S'AA'S ] Note that this procedure for computing d differs from that described in [1]. One can show that the matrix K is equal to the matrix M^[-1]N in that paper. n is an integer variable. On entry n is the dimension of the problem. On exit n is unchanged. m is an integer variable. On entry m is the maximum number of variable metric corrections used to define the limited memory matrix. On exit m is unchanged. nsub is an integer variable. On entry nsub is the number of free variables. On exit nsub is unchanged. ind is an integer array of dimension nsub. On entry ind specifies the coordinate indices of free variables. On exit ind is unchanged. l is a double precision array of dimension n. On entry l is the lower bound of x. On exit l is unchanged. u is a double precision array of dimension n. On entry u is the upper bound of x. On exit u is unchanged. nbd is a integer array of dimension n. 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. x is a double precision array of dimension n. On entry x specifies the Cauchy point xcp. On exit x(i) is the minimizer of Q over the subspace of free variables. d is a double precision array of dimension n. On entry d is the reduced gradient of Q at xcp. On exit d is the Newton direction of Q. ws and wy are double precision arrays; theta is a double precision variable; col is an integer variable; head is an integer variable. On entry they store the information defining the limited memory BFGS matrix: ws(n,m) stores S, a set of s-vectors; wy(n,m) stores Y, a set of y-vectors; theta is the scaling factor specifying B_0 = theta I; col is the number of variable metric corrections stored; head is the location of the 1st s- (or y-) vector in S (or Y). On exit they are unchanged. iword is an integer variable. On entry iword is unspecified. On exit iword specifies the status of the subspace solution. iword = 0 if the solution is in the box, 1 if some bound is encountered. wv is a double precision working array of dimension 2m. wn is a double precision array of dimension 2m x 2m. On entry the upper triangle of wn stores the LEL^T factorization of the indefinite matrix K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] [L_a -R_z theta*S'AA'S ] where E = [-I 0] [ 0 I] On exit wn is unchanged. iprint is an INTEGER variable that must be set by the user. It controls the frequency and type of output generated: iprint.LT.0 no output is generated; iprint=0 print only one line at the last iteration; 0.LT.iprint.LT.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.GT.100 print details of every iteration including x and g; When iprint .GT. 0, the file iterate.dat will be created to summarize the iteration. info is an integer variable. On entry info is unspecified. On exit info = 0 for normal return, = nonzero for abnormal return when the matrix K is ill-conditioned. Subprograms called: Linpack dtrsl. References: [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited memory algorithm for bound constrained optimization'', SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. * * * NEOS, November 1994. (Latest revision June 1996.) Optimization Technology Center. Argonne National Laboratory and Northwestern University. Written by Ciyou Zhu in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. ************

offset_d  Int32

 

WS  Double

and wy are double precision arrays;

offset_ws  Int32

 

WY  Double

 

offset_wy  Int32

 

THETA  Double

is a double precision variable;

COL  Int32

is an integer variable;

HEAD  Int32

is an integer variable. On entry they store the information defining the limited memory BFGS matrix: ws(n,m) stores S, a set of s-vectors; wy(n,m) stores Y, a set of y-vectors; theta is the scaling factor specifying B_0 = theta I; col is the number of variable metric corrections stored; head is the location of the 1st s- (or y-) vector in S (or Y). On exit they are unchanged.

IWORD  Int32

is an integer variable. On entry iword is unspecified. On exit iword specifies the status of the subspace solution. iword = 0 if the solution is in the box, 1 if some bound is encountered.

WV  Double

is a double precision working array of dimension 2m.

offset_wv  Int32

 

WN  Double

is a double precision array of dimension 2m x 2m. On entry the upper triangle of wn stores the LEL^T factorization of the indefinite matrix K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] [L_a -R_z theta*S'AA'S ] where E = [-I 0] [ 0 I] On exit wn is unchanged.

offset_wn  Int32

 

IPRINT  Int32

is an INTEGER variable that must be set by the user. It controls the frequency and type of output generated: iprint.LT.0 no output is generated; iprint=0 print only one line at the last iteration; 0.LT.iprint.LT.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.GT.100 print details of every iteration including x and g; When iprint .GT. 0, the file iterate.dat will be created to summarize the iteration.

INFO  Int32

is an integer variable. On entry info is unspecified. On exit info = 0 for normal return, = nonzero for abnormal return when the matrix K is ill-conditioned.

Reference