psqp_module

PSQP: SQP variable metric method for general nonlinear programming problems.

History

Original Fortran 77 code by Ladislav Luksan.
Jacob Williams, Aug 2017, Significant refactoring to modern Fortran.

Uses

- psqp_matrix_module
- psqp_kind_module
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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Variables

Type	Visibility	Attributes		Name		Initial
integer,	public,	parameter	::	psqp_wp	=	wp	export the working precision

Abstract Interfaces

abstract interface

private subroutine obj_func(me, nf, x, ff)

objective function interface

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer		::	nf	the number of variables
real(kind=wp)		::	x(nf)	a vector of variables
real(kind=wp)		::	ff	the value of the objective function

abstract interface

private subroutine dobj_func(me, nf, x, gf)

gradient of the objective function interface

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer		::	nf	the number of variables
real(kind=wp)		::	x(nf)	a vector of variables
real(kind=wp)		::	gf(nf)	the gradient of the objective function

abstract interface

private subroutine con_func(me, nf, kc, x, fc)

constraint function interface

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer		::	nf	the number of variables
integer		::	kc	the index of the constraint function
real(kind=wp)		::	x(nf)	a vector of variables
real(kind=wp)		::	fc	the value of the constraint function

abstract interface

private subroutine dcon_func(me, nf, kc, x, gc)

gradient of the constraint function interface

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer		::	nf	the number of variables
integer		::	kc	the index of the constraint function
real(kind=wp)		::	x(nf)	a vector of variables and
real(kind=wp)		::	gc(nf)	the gradient of the constraint function

abstract interface

private subroutine report_f(me, iter, x, j, f)

Report function to call once per iteration to report the solution.

Arguments

Type	Intent	Attributes		Name
class(psqp_class),	intent(inout)		::	me
integer,	intent(in)		::	iter	Iteration number
real(kind=wp),	intent(in),	dimension(:)	::	x	optimization variables
real(kind=wp),	intent(in)		::	j	Objective function value
real(kind=wp),	intent(in),	dimension(:)	::	f	Constraint functions

Derived Types

type, public :: psqp_class

The main PSQP class to use.

Components

Type	Visibility	Attributes		Name		Initial
integer,	public		::	nres	=	0	number of restarts.
integer,	public		::	ndec	=	0	number of matrix decomposition.
integer,	public		::	nrem	=	0	number of constraint deletions.
integer,	public		::	nadd	=	0	number of constraint additions.
integer,	public		::	nit	=	0	number of iterations.
integer,	public		::	nfv	=	0	number of function evaluations.
integer,	public		::	nfg	=	0	number of gradient evaluations.
integer,	public		::	nfh	=	0	number of hessian evaluations.
integer,	private		::	mtyp	=	0
integer,	private		::	mode	=	0
integer,	private		::	mes1	=	0
integer,	private		::	mes2	=	0
real(kind=wp),	private		::	rl	=	0.0_wp
real(kind=wp),	private		::	fl	=	0.0_wp
real(kind=wp),	private		::	ru	=	0.0_wp
real(kind=wp),	private		::	fu	=	0.0_wp
real(kind=wp),	private		::	ri	=	0.0_wp
real(kind=wp),	private		::	fi	=	0.0_wp
procedure(obj_func),	private,	pointer	::	obj	=>	null()	objective function
procedure(dobj_func),	private,	pointer	::	dobj	=>	null()	gradient of the objective function
procedure(con_func),	private,	pointer	::	con	=>	null()	constraint function
procedure(dcon_func),	private,	pointer	::	dcon	=>	null()	gradient of the constraint function
procedure(report_f),	private,	pointer	::	report	=>	null()	iteration report function

Type-Bound Procedures

procedure, public :: psqpn
procedure, public :: psqp
procedure, private :: compute_obj_and_dobj
procedure, private :: dual_range_space_quad_prog
procedure, private :: ops_after_constr_deletion
procedure, private :: compute_con_and_dcon
procedure, private :: extended_line_search

Subroutines

private subroutine psqpn(me, nf, nb, nc, x, bound_type, xl, xu, cf, constraint_type, cl, cu, ipar, rpar, f, gmax, cmax, iprnt, iterm, obj, dobj, con, dcon, report)

Date: 97/01/22

easy to use subroutine for general nonlinear programming problems.

Arguments

Type	Intent	Optional	Attributes		Name
class(psqp_class),	intent(inout)			::	me
integer,	intent(in)			::	nf	number of variables
integer,	intent(in)			::	nb	choice of simple bounds. Read more…
integer,	intent(in)			::	nc	number of general nonlinear constraints.
real(kind=wp),	intent(inout),		dimension(nf)	::	x	x(nf) vector of variables.
integer,	intent(in),		dimension(nf)	::	bound_type	ix(nf) vector containing types of bounds. Read more…
real(kind=wp),	intent(in),		dimension(nf)	::	xl	xl(nf) vector containing lower bounds for variables.
real(kind=wp),	intent(in),		dimension(nf)	::	xu	xu(nf) vector containing upper bounds for variables.
real(kind=wp),	intent(out),		dimension(nc+1)	::	cf	cf(nc+1) vector containing values of the constraint functions.
integer,	intent(in),		dimension(nc)	::	constraint_type	ic(nc) vector containing types of constraints: Read more…
real(kind=wp),	intent(in),		dimension(nc)	::	cl	cl(nc) vector containing lower bounds for constraint functions.
real(kind=wp),	intent(in),		dimension(nc)	::	cu	cu(nc) vector containing upper bounds for constraint functions.
integer,	intent(in),		dimension(6)	::	ipar	integer paremeters: Read more…
real(kind=wp),	intent(in),		dimension(5)	::	rpar	real parameters: Read more…
real(kind=wp),	intent(out)			::	f	value of the objective function.
real(kind=wp),	intent(out)			::	gmax	maximum partial derivative of the lagrangian function.
real(kind=wp),	intent(out)			::	cmax	maximum constraint violation.
integer,	intent(in)			::	iprnt	print specification: Read more…
integer,	intent(out)			::	iterm	variable that indicates the cause of termination. Read more…
procedure(obj_func)				::	obj	computation of the value of the objective function
procedure(dobj_func)				::	dobj	computation of the gradient of the objective function
procedure(con_func)				::	con	computation of the value of the constraint function
procedure(dcon_func)				::	dcon	computation of the gradient of the constraint function
procedure(report_f),		optional		::	report	iteration report function. Note: this is independent of `iprnt`. If this function is associated, each iteration will be reported

private subroutine psqp(me, nf, nb, nc, x, ix, xl, xu, cf, ic, cl, cu, cg, cfo, cfd, gc, ica, cr, cz, cp, gf, g, h, s, xo, go, xmax, tolx, tolc, tolg, rpf, cmax, gmax, f, mit, mfv, met, mec, iprnt, iterm)

Date: 97/01/22

recursive quadratic programming method with the bfgs variable metric update for general nonlinear programming problems.

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer		::	nf	number of variables.
integer		::	nb	choice of simple bounds. Read more…
integer		::	nc	number of linear constraints.
real(kind=wp)		::	x(*)	x(nf) vector of variables.
integer,	intent(inout)	::	ix(*)	ix(nf) vector containing types of bounds. Read more…
real(kind=wp)		::	xl(*)	xl(nf) vector containing lower bounds for variables.
real(kind=wp)		::	xu(*)	xu(nf) vector containing upper bounds for variables.
real(kind=wp)		::	cf(*)	cf(nc+1) vector containing values of the constraint functions.
integer,	intent(inout)	::	ic(*)	ic(nc) vector containing types of constraints. Read more…
real(kind=wp)		::	cl(*)	cl(nc) vector containing lower bounds for constraint functions.
real(kind=wp)		::	cu(*)	cu(nc) vector containing upper bounds for constraint functions.
real(kind=wp)		::	cg(*)	cg(nf*nc) matrix whose columns are normals of the linear constraints.
real(kind=wp)		::	cfo(*)	cfo(nc) vector containing saved values of the constraint functions.
real(kind=wp)		::	cfd(*)	cfd(nc) vector containing increments of the constraint functions.
real(kind=wp)		::	gc(*)	gc(nf) gradient of the selected constraint function.
integer		::	ica(*)	ica(nf) vector containing indices of active constraints.
real(kind=wp)		::	cr(*)	cr(nf*(nf+1)/2) triangular decomposition of kernel of the orthogonal projection.
real(kind=wp)		::	cz(*)	cz(nf) vector of lagrange multipliers.
real(kind=wp)		::	cp(*)
real(kind=wp)		::	gf(*)	gf(nf) gradient of the model function.
real(kind=wp)		::	g(*)	g(nf) gradient of the objective function.
real(kind=wp)		::	h(*)	h(nf*(nf+1)/2) triangular decomposition or inversion of the hessian matrix approximation.
real(kind=wp)		::	s(*)	s(nf) direction vector.
real(kind=wp)		::	xo(*)	xo(nf) vectors of variables difference.
real(kind=wp)		::	go(*)	go(nf) gradients difference.
real(kind=wp)		::	xmax	maximum stepsize.
real(kind=wp)		::	tolx	tolerance for change of variables.
real(kind=wp)		::	tolc	tolerance for constraint violations.
real(kind=wp)		::	tolg	tolerance for the gradient of the lagrangian function.
real(kind=wp)		::	rpf	penalty coefficient.
real(kind=wp)		::	cmax	maximum constraint violation.
real(kind=wp)		::	gmax	maximum partial derivative of the lagrangian function.
real(kind=wp)		::	f	value of the objective function.
integer		::	mit	maximum number of iterations.
integer		::	mfv	maximum number of function evaluations.
integer		::	met	variable metric update used. Read more…
integer		::	mec	correction if the negative curvature occurs. Read more…
integer		::	iprnt	print specification. Read more…
integer		::	iterm	variable that indicates the cause of termination. Read more…

private subroutine compute_con_and_dcon(me, nf, nc, x, fc, cf, cl, cu, ic, gc, cg, cmax, kd, ld)

Date: 97/12/01

computation of the value and the gradient of the constraint function.

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer		::	nf	number of variables.
integer		::	nc	number of constraints.
real(kind=wp)		::	x(nf)	x(nf) vector of variables.
real(kind=wp)		::	fc	value of the selected constraint function.
real(kind=wp)		::	cf(*)	cf(nc) vector containing values of constraint functions.
real(kind=wp)		::	cl(*)	cl(nc) vector containing lower bounds for constraint functions.
real(kind=wp)		::	cu(*)	cu(nc) vector containing upper bounds for constraint functions.
integer		::	ic(*)	ic(nc) vector containing types of constraints.
real(kind=wp)		::	gc(nf)	gc(nf) gradient of the selected constraint function.
real(kind=wp)		::	cg(*)	cg(nf*nc) matrix whose columns are gradients of constraint functions.
real(kind=wp)		::	cmax	maximum constraint violation.
integer		::	kd	degree of required derivatives.
integer		::	ld	degree of previously computed derivatives.

private subroutine compute_obj_and_dobj(me, nf, x, gf, g, ff, f, kd, ld, iext)

Date: 97/12/01

computation of the value and the gradient of the objective function.

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer,	intent(in)	::	nf	number of variables.
real(kind=wp),	intent(in)	::	x(nf)	x(nf) vector of variables.
real(kind=wp),	intent(out)	::	gf(nf)	gf(nf) gradient of the model function.
real(kind=wp),	intent(out)	::	g(nf)	g(nf) gradient of the objective function.
real(kind=wp),	intent(out)	::	ff	value of the model function.
real(kind=wp),	intent(out)	::	f	value of the objective function.
integer,	intent(in)	::	kd	degree of required derivatives.
integer,	intent(inout)	::	ld	degree of previously computed derivatives.
integer,	intent(in)	::	iext	type of extremum. Read more…

private subroutine dual_range_space_quad_prog(me, nf, nc, x, ix, xl, xu, cf, cfd, ic, ica, cl, cu, cg, cr, cz, g, go, h, s, mfp, kbf, kbc, idecf, eta2, eta9, eps7, eps9, umax, gmax, n, iterq)

Date: 97/12/01

dual range space quadratic programming method.

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer		::	nf	number of variables.
integer		::	nc	number of linear constraints.
real(kind=wp)		::	x(*)	x(nf) vector of variables.
integer		::	ix(*)	ix(nf) vector containing types of bounds.
real(kind=wp)		::	xl(*)	xl(nf) vector containing lower bounds for variables.
real(kind=wp)		::	xu(*)	xu(nf) vector containing upper bounds for variables.
real(kind=wp)		::	cf(*)	cf(nf) vector containing values of the constraint functions.
real(kind=wp)		::	cfd(*)	cfd(nc) vector containing increments of the constraint functions.
integer		::	ic(*)	ic(nc) vector containing types of constraints.
integer		::	ica(*)	ica(nf) vector containing indices of active constraints.
real(kind=wp)		::	cl(*)	cl(nc) vector containing lower bounds for constraint functions.
real(kind=wp)		::	cu(*)	cu(nc) vector containing upper bounds for constraint functions.
real(kind=wp)		::	cg(*)	cg(nf*nc) matrix whose columns are normals of the linear constraints.
real(kind=wp)		::	cr(*)	cr(nf*(nf+1)/2) triangular decomposition of kernel of the orthogonal projection.
real(kind=wp)		::	cz(*)	cz(nf) vector of lagrange multipliers.
real(kind=wp)		::	g(*)	g(nf) gradient of the lagrangian function.
real(kind=wp)		::	go(*)	go(nf) saved gradient of the objective function.
real(kind=wp)		::	h(*)	h(nf*(nf+1)/2) triangular decomposition or inversion of the hessian matrix approximation.
real(kind=wp)		::	s(*)	s(nf) direction vector.
integer		::	mfp	type of feasible point. Read more…
integer		::	kbf	specification of simple bounds. Read more…
integer		::	kbc	specification of linear constraints. Read more…
integer		::	idecf	decomposition indicator. Read more…
real(kind=wp)		::	eta2	tolerance for positive definiteness of the hessian matrix.
real(kind=wp)		::	eta9	maximum for real numbers.
real(kind=wp)		::	eps7	tolerance for linear independence of constraints.
real(kind=wp)		::	eps9	tolerance for activity of constraints.
real(kind=wp)		::	umax	maximum absolute value of a negative lagrange multiplier.
real(kind=wp)		::	gmax	maximum absolute value of a partial derivative.
integer		::	n	dimension of the manifold defined by active constraints.
integer		::	iterq	type of feasible point. Read more…

private subroutine update_tri_decomp_general(nf, n, ica, cg, cr, h, s, g, eps7, gmax, umax, idecf, inew, nadd, ier, job)

Date: 97/12/01

triangular decomposition of kernel of the general projection is updated after constraint addition.

Arguments

Type		Name
integer	::	nf	declared number of variables.
integer	::	n	actual number of variables.
integer	::	ica(*)	ica(nf) vector containing indices of active constraints.
real(kind=wp)	::	cg(*)	cg(nf*nc) matrix whose columns are normals of the linear constraints.
real(kind=wp)	::	cr(*)	cr(nf*(nf+1)/2) triangular decomposition of kernel of the orthogonal projection.
real(kind=wp)	::	h(*)	h(nf*(nf+1)/2) triangular decomposition or inversion of the hessian matrix approximation.
real(kind=wp)	::	s(*)	s(nf) auxiliary vector.
real(kind=wp)	::	g(*)	g(nf) vector used in the dual range space quadratic programming method.
real(kind=wp)	::	eps7	tolerance for linear independence of constraints.
real(kind=wp)	::	gmax	maximum absolute value of a partial derivative.
real(kind=wp)	::	umax	maximum absolute value of a negative lagrange multiplier.
integer	::	idecf	decomposition indicator. Read more…
integer	::	inew	index of the new active constraint.
integer	::	nadd	number of constraint additions.
integer	::	ier	error indicator.
integer	::	job	specification of computation. output vector g is not or is computed in case when n<=0 if job=0 or job=1 respectively.

private subroutine determine_new_active_linear_constr(nf, nc, cf, cfd, ic, cl, cu, cg, s, eps9, par, kbc, inew, knew)

Date: 97/12/01

determination of the new active linear constraint.

Arguments

Type		Name
integer	::	nf	number of variables.
integer	::	nc	number of constraints.
real(kind=wp)	::	cf(*)	cf(nc) vector containing values of the constraint functions.
real(kind=wp)	::	cfd(*)	cfd(nc) vector containing increments of the constraint functions.
integer	::	ic(*)	ic(nc) vector containing types of constraints.
real(kind=wp)	::	cl(*)	cl(nc) vector containing lower bounds for constraint functions.
real(kind=wp)	::	cu(*)	cu(nc) vector containing upper bounds for constraint functions.
real(kind=wp)	::	cg(*)	cg(nf*nc) matrix whose columns are normals of the linear constraints.
real(kind=wp)	::	s(*)	s(nf) direction vector.
real(kind=wp)	::	eps9	tolerance for active constraints.
real(kind=wp)	::	par	auxiliary variable.
integer	::	kbc	specification of linear constraints. Read more…
integer	::	inew	index of the new active constraint.
integer	::	knew	signum of the new active normal.

private subroutine determine_new_active_simple_bound(nf, ix, xo, xl, xu, s, kbf, inew, knew, eps9, par)

Date: 91/12/01

determination of the new active simple bound.

Arguments

Type		Name
integer	::	nf	declared number of variables.
integer	::	ix(*)	ix(nf) vector containing types of bounds.
real(kind=wp)	::	xo(*)	xo(nf) saved vector of variables.
real(kind=wp)	::	xl(*)	xl(nf) vector containing lower bounds for variables.
real(kind=wp)	::	xu(*)	xu(nf) vector containing upper bounds for variables.
real(kind=wp)	::	s(*)	s(nf) direction vector.
integer	::	kbf	specification of simple bounds. Read more…
integer	::	inew	index of the new active constraint.
integer	::	knew	signum of the new normal.
real(kind=wp)	::	eps9	tolerance for active constraints.
real(kind=wp)	::	par	auxiliary variable.

private subroutine test_simple_bound(x, ix, xl, xu, eps9, i)

Date: 97/12/01

test on activity of a given simple bound.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x(*)	x(nf) vector of variables.
integer,	intent(inout)	::	ix(*)	ix(nf) vector containing types of bounds.
real(kind=wp),	intent(in)	::	xl(*)	xl(nf) vector containing lower bounds for variables.
real(kind=wp),	intent(in)	::	xu(*)	xu(nf) vector containing upper bounds for variables.
real(kind=wp),	intent(in)	::	eps9	tolerance for active constraints.
integer,	intent(in)	::	i	index of tested simple bound.

private subroutine transform_incompatible_qp_subproblem(nc, cf, ic, cl, cu, kbc)

Date: 98/12/01

transformation of the incompatible quadratic programming subproblem.

Arguments

Type		Name
integer	::	nc	number of current linear constraints.
real(kind=wp)	::	cf(*)	cf(nf) vector containing values of the constraint functions.
integer	::	ic(nc)	ic(nc) vector containing types of constraints.
real(kind=wp)	::	cl(*)	cl(nc) vector containing lower bounds for constraint functions.
real(kind=wp)	::	cu(*)	cu(nc) vector containing upper bounds for constraint functions.
integer	::	kbc	specification of linear constraints. Read more…

private subroutine ops_after_constr_deletion(me, nf, nc, ix, ia, iaa, ar, ic, s, n, iold, krem, ier)

Date: 91/12/01

operations after constraint deletion.

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
integer		::	nf	declared number of variables.
integer		::	nc	number of constraints.
integer		::	ix(*)	ix(nf) vector containing types of bounds.
integer		::	ia(*)	ia(na) vector containing types of deviations.
integer		::	iaa(*)	iaa(nf+1) vector containing indices of active functions.
real(kind=wp)		::	ar(*)	ar((nf+1)*(nf+2)/2) triangular decomposition of kernel of the orthogonal projection.
integer		::	ic(*)	ic(nc) vector containing types of constraints.
real(kind=wp)		::	s(*)	s(nf+1) auxiliary vector.
integer		::	n	actual number of variables.
integer		::	iold	index of the old active constraint.
integer		::	krem	auxiliary variable.
integer		::	ier	error indicator.

private subroutine update_tri_decomp_orthogonal(nf, ica, cr, g, n, iold, krem, ier)

Date: 91/12/01

triangular decomposition of kernel of the orthogonal projection is updated after constraint deletion.

Arguments

Type		Name
integer	::	nf	declared number of variables.
integer	::	ica(*)	ica(nf) vector containing indices of active constraints.
real(kind=wp)	::	cr(*)	cr(nf*(nf+1)/2) triangular decomposition of kernel of the orthogonal projection.
real(kind=wp)	::	g(*)	g(nf) auxiliary vector.
integer	::	n	actual number of variables.
integer	::	iold	index of the old active constraint.
integer	::	krem	auxiliary variable.
integer	::	ier	error indicator.

private subroutine line_search_interpolation(ro, rl, ru, ri, fo, fl, fu, fi, po, r, mode, mtyp, merr)

Date: 91/12/01

extrapolation or interpolation for line search without directional derivatives.

Arguments

Type		Name
real(kind=wp)	::	ro	initial value of the stepsize parameter.
real(kind=wp)	::	rl	lower value of the stepsize parameter.
real(kind=wp)	::	ru	upper value of the stepsize parameter.
real(kind=wp)	::	ri	inner value of the stepsize parameter.
real(kind=wp)	::	fo	value of the objective function for r=ro.
real(kind=wp)	::	fl	value of the objective function for r=rl.
real(kind=wp)	::	fu	value of the objective function for r=ru.
real(kind=wp)	::	fi	value of the objective function for r=ri.
real(kind=wp)	::	po	initial value of the directional derivative.
real(kind=wp)	::	r	value of the stepsize parameter obtained.
integer	::	mode	mode of line search.
integer	::	mtyp	method selection Read more…
integer	::	merr	error indicator. merr=0 for normal return.

private pure subroutine compute_augmented_lagrangian(nf, n, nc, cf, ic, ica, cl, cu, cz, rpf, fc, f)

Date: 97/12/01

computation of value of the augmented lagrangian function.

Arguments

Type	Intent		Name
integer,	intent(in)	::	nf	number of variables.
integer,	intent(in)	::	n	dimension of the constraint null space.
integer,	intent(in)	::	nc	number of constraints.
real(kind=wp),	intent(in)	::	cf(*)	cf(nc+1) vector containing values of the constraints.
integer,	intent(in)	::	ic(*)	ic(nc) vector containing types of constraints.
integer,	intent(in)	::	ica(*)	ica(nf) vector containing indices of active constraints.
real(kind=wp),	intent(in)	::	cl(*)	cl(nc) vector containing lower bounds for constraint functions.
real(kind=wp),	intent(in)	::	cu(*)	cu(nc) vector containing upper bounds for constraint functions.
real(kind=wp),	intent(in)	::	cz(*)	cz(nc) vector of lagrange multipliers.
real(kind=wp),	intent(in)	::	rpf	penalty coefficient.
real(kind=wp),	intent(out)	::	fc	value of the penalty term.
real(kind=wp),	intent(out)	::	f	value of the penalty function.

private pure subroutine compute_new_penalty_parameters(nf, n, nc, ica, cz, cp)

Date: 97/12/01

computation of the new penalty parameters.

Arguments

Type	Intent		Name
integer,	intent(in)	::	nf	declared number of variables.
integer,	intent(in)	::	n	actual number of variables.
integer,	intent(in)	::	nc	number of constraints.
integer,	intent(in)	::	ica(*)	vector containing indices of active constraints.
real(kind=wp),	intent(in)	::	cz(*)	vector of lagrange multipliers.
real(kind=wp),	intent(inout)	::	cp(*)	vector containing penalty parameters.

private subroutine extended_line_search(me, r, ro, rp, f, fo, fp, po, pp, fmin, fmax, rmin, rmax, tols, kd, ld, nit, kit, nred, mred, maxst, iest, inits, iters, kters, mes, isys)

Date: 97/12/01

extended line search without directional derivatives.

Arguments

Type	Intent		Name
class(psqp_class),	intent(inout)	::	me
real(kind=wp)		::	r	value of the stepsize parameter.
real(kind=wp)		::	ro	initial value of the stepsize parameter.
real(kind=wp)		::	rp	previous value of the stepsize parameter.
real(kind=wp)		::	f	value of the objective function.
real(kind=wp)		::	fo	initial value of the objective function.
real(kind=wp)		::	fp	previous value of the objective function.
real(kind=wp)		::	po	initial value of the directional derivative.
real(kind=wp)		::	pp	previous value of the directional derivative.
real(kind=wp)		::	fmin	lower bound for value of the objective function.
real(kind=wp)		::	fmax	upper bound for value of the objective function.
real(kind=wp)		::	rmin	minimum value of the stepsize parameter
real(kind=wp)		::	rmax	maximum value of the stepsize parameter
real(kind=wp)		::	tols	termination tolerance for line search (in test on the change of the function value).
integer		::	kd	degree of required dervatives.
integer		::	ld	degree of previously computed derivatives.
integer		::	nit	actual number of iterations.
integer		::	kit	number of the iteration after last restart.
integer		::	nred	actual number of extrapolations or interpolations.
integer		::	mred	maximum number of extrapolations or interpolations.
integer		::	maxst	maximum stepsize indicator. maxst=0 or maxst=1 if maximum stepsize was not or was reached.
integer		::	iest	lower bound specification. iest=0 or iest=1 if lower bound is not or is given.
integer		::	inits	choice of the initial stepsize. Read more…
integer		::	iters	termination indicator. Read more…
integer		::	kters	termination selection. Read more…
integer		::	mes	method selection. Read more…
integer		::	isys	control parameter.

private subroutine bfgs_variable_metric_update(n, h, g, s, xo, go, r, po, nit, kit, iterh, met, met1, mec)

Date: 92/12/01

variable metric update of a dense symmetric positive definite matrix using the factorization b=ldtrans(l).

Arguments

Type		Name
integer	::	n	actual number of variables.
real(kind=wp)	::	h(*)	h(m) factorization b=ldtrans(l) of a positive definite approximation of the hessian matrix.
real(kind=wp)	::	g(*)	g(nf) gradient of the objective function.
real(kind=wp)	::	s(*)	s(nf) auxiliary vector.
real(kind=wp)	::	xo(*)	xo(nf) vectors of variables difference.
real(kind=wp)	::	go(*)	go(nf) gradients difference.
real(kind=wp)	::	r	value of the stepsize parameter.
real(kind=wp)	::	po	old value of the directional derivative.
integer	::	nit	actual number of iterations.
integer	::	kit	number of the iteration after last restart.
integer	::	iterh	termination indicator. Read more…
integer	::	met
integer	::	met1	selection of self scaling. Read more…
integer	::	mec	correction if the negative curvature occurs. Read more…

private subroutine dual_range_space_qp(nf, n, x, xo, ica, cg, cz, g, go, r, f, fo, p, po, cmax, cmaxo, dmax, kd, ld, iters)

Date: 91/12/01

dual range space quadratic programming method for minimax approximation.

Arguments

Type	Intent		Name
integer,	intent(in)	::	nf	declared number of variables.
integer,	intent(inout)	::	n	actual number of variables.
real(kind=wp)		::	x(*)	x(nf) vector of variables.
real(kind=wp)		::	xo(*)	xo(nf) saved vector of variables.
integer,	intent(in)	::	ica(*)	ica(nf) vector containing indices of active constraints.
real(kind=wp)		::	cg(*)	cg(nf*nc) matrix whose columns are normals of the linear constraints.
real(kind=wp)		::	cz(*)	cz(nf) vector of lagrange multipliers.
real(kind=wp)		::	g(*)	g(nf) gradient of the lagrangian function.
real(kind=wp)		::	go(*)	go(nf) saved gradient of the lagrangian function.
real(kind=wp)		::	r	value of the stepsize parameter.
real(kind=wp)		::	f	new value of the objective function.
real(kind=wp)		::	fo	old value of the objective function.
real(kind=wp)		::	p	new value of the directional derivative.
real(kind=wp)		::	po	old value of the directional derivative.
real(kind=wp)		::	cmax	value of the constraint violation.
real(kind=wp)		::	cmaxo	saved value of the constraint violation.
real(kind=wp),	intent(out)	::	dmax	maximum relative difference of variables.
integer		::	kd
integer		::	ld
integer		::	iters	termination indicator for steplength determination. iters=0 for zero step.

psqp_module Module

Contents

Variables

Abstract Interfaces

Derived Types

Subroutines

History

Uses

Variables

Abstract Interfaces

abstract interface

private subroutine obj_func(me, nf, x, ff)

Arguments

abstract interface

private subroutine dobj_func(me, nf, x, gf)

Arguments

abstract interface

private subroutine con_func(me, nf, kc, x, fc)

Arguments

abstract interface

private subroutine dcon_func(me, nf, kc, x, gc)

Arguments

abstract interface

private subroutine report_f(me, iter, x, j, f)

Arguments

Derived Types

type, public :: psqp_class

Components

Type-Bound Procedures

Subroutines

private subroutine psqpn(me, nf, nb, nc, x, bound_type, xl, xu, cf, constraint_type, cl, cu, ipar, rpar, f, gmax, cmax, iprnt, iterm, obj, dobj, con, dcon, report)

Arguments

private subroutine psqp(me, nf, nb, nc, x, ix, xl, xu, cf, ic, cl, cu, cg, cfo, cfd, gc, ica, cr, cz, cp, gf, g, h, s, xo, go, xmax, tolx, tolc, tolg, rpf, cmax, gmax, f, mit, mfv, met, mec, iprnt, iterm)

Arguments

private subroutine compute_con_and_dcon(me, nf, nc, x, fc, cf, cl, cu, ic, gc, cg, cmax, kd, ld)

Arguments

private subroutine compute_obj_and_dobj(me, nf, x, gf, g, ff, f, kd, ld, iext)

Arguments

private subroutine dual_range_space_quad_prog(me, nf, nc, x, ix, xl, xu, cf, cfd, ic, ica, cl, cu, cg, cr, cz, g, go, h, s, mfp, kbf, kbc, idecf, eta2, eta9, eps7, eps9, umax, gmax, n, iterq)

Arguments

private subroutine update_tri_decomp_general(nf, n, ica, cg, cr, h, s, g, eps7, gmax, umax, idecf, inew, nadd, ier, job)

Arguments

private subroutine determine_new_active_linear_constr(nf, nc, cf, cfd, ic, cl, cu, cg, s, eps9, par, kbc, inew, knew)

Arguments

private subroutine determine_new_active_simple_bound(nf, ix, xo, xl, xu, s, kbf, inew, knew, eps9, par)

Arguments

private subroutine test_simple_bound(x, ix, xl, xu, eps9, i)

Arguments

private subroutine transform_incompatible_qp_subproblem(nc, cf, ic, cl, cu, kbc)

Arguments

private subroutine ops_after_constr_deletion(me, nf, nc, ix, ia, iaa, ar, ic, s, n, iold, krem, ier)

Arguments

private subroutine update_tri_decomp_orthogonal(nf, ica, cr, g, n, iold, krem, ier)

Arguments

private subroutine line_search_interpolation(ro, rl, ru, ri, fo, fl, fu, fi, po, r, mode, mtyp, merr)

Arguments

private pure subroutine compute_augmented_lagrangian(nf, n, nc, cf, ic, ica, cl, cu, cz, rpf, fc, f)

Arguments

private pure subroutine compute_new_penalty_parameters(nf, n, nc, ica, cz, cp)

Arguments

private subroutine extended_line_search(me, r, ro, rp, f, fo, fp, po, pp, fmin, fmax, rmin, rmax, tols, kd, ld, nit, kit, nred, mred, maxst, iest, inits, iters, kters, mes, isys)

Arguments

private subroutine bfgs_variable_metric_update(n, h, g, s, xo, go, r, po, nit, kit, iterh, met, met1, mec)

Arguments

private subroutine dual_range_space_qp(nf, n, x, xo, ica, cg, cz, g, go, r, f, fo, p, po, cmax, cmaxo, dmax, kd, ld, iters)

Arguments