NAG AD Library
e04kf (handle_solve_bounds_foas)

e04kf is the AD Library version of the primal routine e04kff. Based (in the C++ interface) on overload resolution, e04kf can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e04kf_AD_f (

ad_handle, handle, objfun, objgrd, monit, nvar, x, rinfo, stats, iuser, ruser, cpuser, ifail)

Integer, Intent (In)	::	nvar
Integer, Intent (Inout)	::	iuser(*), ifail
ADTYPE, Intent (Inout)	::	x(nvar), ruser(*)
ADTYPE, Intent (Out)	::	rinfo(100), stats(100)
Type (c_ptr), Intent (Inout)	::	ad_handle
Type (c_ptr), Intent (In)	::	handle, cpuser
External	::	objfun, objgrd, monit

Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:

when ADTYPE is	Real(kind=nag_wp)	then AD is p0w
when ADTYPE is	Type(nagad_a1w_w_rtype)	then AD is a1w
when ADTYPE is	Type(nagad_t1w_w_rtype)	then AD is t1w

C++ Header Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void e04kf (

void *&ad_handle, void *handle,
void (NAG_CALL objfun)(void *&ad_handle, const Integer &nvar, const ADTYPE x[], ADTYPE &fx, Integer &inform, Integer iuser[], ADTYPE ruser[], void *cpuser),
void (NAG_CALL objgrd)(void *&ad_handle, const Integer &nvar, const ADTYPE x[], const Integer &nnzfd, ADTYPE fdx[], Integer &inform, Integer iuser[], ADTYPE ruser[], void *cpuser),
void (NAG_CALL monit)(void *&ad_handle, const Integer &nvar, const ADTYPE x[], Integer &inform, const ADTYPE rinfo[], const ADTYPE stats[], Integer iuser[], ADTYPE ruser[], void *cpuser),
const Integer &nvar, ADTYPE x[], ADTYPE rinfo[], ADTYPE stats[], const Integer &liuser, Integer iuser[], const Integer &lruser, ADTYPE ruser[], void *cpuser, Integer &ifail)

}
}

The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types:
double,
dco::ga1s<double>::type,
dco::gt1s<double>::type

Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

e04kf is the AD Library version of the primal routine e04kff.

e04kff is a solver from the NAG optimization modelling suite for bound-constrained large-scale Nonlinear Programming (NLP) problems. It is a first-order active-set method (FOAS) that has low memory requirements and thus is suitable for very large-scale problems. For further information see Section 3 in the documentation for e04kff.

4 References

Dai Y-H and Kou C-X (2013) A Nonlinear Conjugate Gradient Algorithm with an Optimal Property and an Improved Wolfe Line Search SIAM J. Optim. 23(1) 296–320

Gill P E and Leonard M W (2003) Limited-Memory Reduced-Hessian Methods for Large-Scale Unconstrained Optimization SIAM J. Optim. 14(2) 380–401

Hager W W and Zhang H (2005) A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search SIAM J. Optim. 16(1) 170–192

Hager W W and Zhang H (2006a) Algorithm 851: CG DESCENT, a Conjugate Gradient Method with Guaranteed Descent ACM Trans. Math. Software 32(1) 113–137

Hager W W and Zhang H (2006b) A New Active Set Algorithm for Box Constrained Optimization SIAM J. Optim. 17(2) 525–557

Hager W W and Zhang H (2013) The Limited Memory Conjugate Gradient Method SIAM J. Optim. 23(4) 2150–2168

Nocedal J and Wright S J (2006) Numerical Optimization (2nd Edition) Springer Series in Operations Research, Springer, New York

5 Arguments

In addition to the arguments present in the interface of the primal routine, e04kf includes some arguments specific to AD.

A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine. A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.

1: ad_handle – Pointer to AD Data Input/Output

On entry: a handle to the AD configuration data object, as created by x10aa.

2: handle – Type(c_ptr) Input

3: objfun – Subroutine External Procedure

If a null pointer is used as the argument, then a NAG supplied routine will be used as the argument for this parameter (C++ only). For the Fortran interface, the NAG supplied routine e04kf_AD_v may be used as the actual argument for this parameter.

The specification of objfun is:

Fortran Interface

Subroutine objfun (

ad_handle, nvar, x, fx, inform, iuser, ruser, cpuser)

Integer, Intent (In)	::	nvar
Integer, Intent (Inout)	::	inform, iuser(*)
ADTYPE, Intent (In)	::	x(nvar)
ADTYPE, Intent (Inout)	::	ruser(*)
ADTYPE, Intent (Out)	::	fx
Type (c_ptr), Intent (Inout)	::	ad_handle
Type (c_ptr), Intent (In)	::	cpuser

C++ Header Interface

void objfun (

void *&ad_handle, const Integer &nvar, const ADTYPE x[], ADTYPE &fx, Integer &inform, Integer iuser[], ADTYPE ruser[], void *cpuser)

1: ad_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object.
2: nvar – Integer Input
3: x – ADTYPE array Input
4: fx – ADTYPE Output
5: inform – Integer Input/Output
6: iuser – Integer array User Workspace
7: ruser – ADTYPE array User Workspace
8: cpuser – Type(c_ptr) User Workspace

4: objgrd – Subroutine External Procedure

If a null pointer is used as the argument, then a NAG supplied routine will be used as the argument for this parameter (C++ only). For the Fortran interface, the NAG supplied routine e04kf_AD_w may be used as the actual argument for this parameter.

The specification of objgrd is:

Fortran Interface

Subroutine objgrd (

ad_handle, nvar, x, nnzfd, fdx, inform, iuser, ruser, cpuser)

Integer, Intent (In)	::	nvar, nnzfd
Integer, Intent (Inout)	::	inform, iuser(*)
ADTYPE, Intent (In)	::	x(nvar)
ADTYPE, Intent (Inout)	::	fdx(nnzfd), ruser(*)
Type (c_ptr), Intent (Inout)	::	ad_handle
Type (c_ptr), Intent (In)	::	cpuser

C++ Header Interface

void objgrd (

void *&ad_handle, const Integer &nvar, const ADTYPE x[], const Integer &nnzfd, ADTYPE fdx[], Integer &inform, Integer iuser[], ADTYPE ruser[], void *cpuser)

1: ad_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object.
2: nvar – Integer Input
3: x – ADTYPE array Input
4: nnzfd – Integer Input
5: fdx – ADTYPE array Input/Output
6: inform – Integer Input/Output
7: iuser – Integer array User Workspace
8: ruser – ADTYPE array User Workspace
9: cpuser – Type(c_ptr) User Workspace

5: monit – Subroutine External Procedure

If a null pointer is used as the argument, then a NAG supplied routine will be used as the argument for this parameter (C++ only). For the Fortran interface, the NAG supplied routine e04kf_AD_u may be used as the actual argument for this parameter.

The specification of monit is:

Fortran Interface

Subroutine monit (

ad_handle, nvar, x, inform, rinfo, stats, iuser, ruser, cpuser)

Integer, Intent (In)	::	nvar
Integer, Intent (Inout)	::	inform, iuser(*)
ADTYPE, Intent (In)	::	x(nvar), rinfo(100), stats(100)
ADTYPE, Intent (Inout)	::	ruser(*)
Type (c_ptr), Intent (Inout)	::	ad_handle
Type (c_ptr), Intent (In)	::	cpuser

C++ Header Interface

void monit (

void *&ad_handle, const Integer &nvar, const ADTYPE x[], Integer &inform, const ADTYPE rinfo[], const ADTYPE stats[], Integer iuser[], ADTYPE ruser[], void *cpuser)

1: ad_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object.
2: nvar – Integer Input
3: x – ADTYPE array Input
4: inform – Integer Input/Output
5: rinfo – ADTYPE array Input
6: stats – ADTYPE array Input
7: iuser – Integer array User Workspace
8: ruser – ADTYPE array User Workspace
9: cpuser – Type(c_ptr) User Workspace

6: nvar – Integer Input

7: x(nvar) – ADTYPE array Input/Output

8: rinfo( $100$ ) – ADTYPE array Output

9: stats( $100$ ) – ADTYPE array Output

10: liuser Input

User workspace dimension (C++ only), see x10af to specify the dimension from Fortran.

11: iuser( $*$ ) – Integer array User Workspace

12: lruser Input

User workspace dimension (C++ only), see x10ae to specify the dimension from Fortran.

13: ruser( $*$ ) – ADTYPE array User Workspace

14: cpuser – Type(c_ptr) User Workspace

15: ifail – Integer Input/Output

6 Error Indicators and Warnings

e04kf preserves all error codes from e04kff and in addition can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: A C++ exception was thrown.
The error message will show the details of the C++ exception text.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e04kf is not threaded in any implementation.

9 Further Comments

None.

10 Example

A NAG AD Library example is not yet available, please refer to the NAG AD Library Introduction for information on calling routines from the AD Library.

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E04 (Opt) Chapter Contents

E04 (Opt) Chapter Introduction (FL)

e04kf: FL CL CPP AD

NAG AD Librarye04kf (handle_solve_bounds_foas)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

NAG AD Library
e04kf (handle_solve_bounds_foas)