psqp_class Derived Type

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

  • 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 IntentOptional 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

procedure, public :: psqp

  • 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.

    Read more…

    Arguments

    Type IntentOptional Attributes 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…

procedure, private :: compute_obj_and_dobj

  • 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.

    Read more…

    Arguments

    Type IntentOptional Attributes 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…

procedure, private :: dual_range_space_quad_prog

  • 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.

    Read more…

    Arguments

    Type IntentOptional Attributes 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…

procedure, private :: ops_after_constr_deletion

  • 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.

    Read more…

    Arguments

    Type IntentOptional Attributes 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.

procedure, private :: compute_con_and_dcon

  • 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.

    Read more…

    Arguments

    Type IntentOptional Attributes 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.

procedure, private :: extended_line_search

  • 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.

    Read more…

    Arguments

    Type IntentOptional Attributes 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.

Source Code

   type, public :: psqp_class

      !! The main PSQP class to use.

      private

      ! these were formerly in the `stat` common block:
      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.

      ! formerly saved variables in extended_line_search:
      integer  :: mtyp = 0
      integer  :: mode = 0
      integer  :: mes1 = 0
      integer  :: mes2 = 0
      real(wp) :: rl = 0.0_wp
      real(wp) :: fl = 0.0_wp
      real(wp) :: ru = 0.0_wp
      real(wp) :: fu = 0.0_wp
      real(wp) :: ri = 0.0_wp
      real(wp) :: fi = 0.0_wp

      procedure(obj_func), pointer  :: obj  => null() !! objective function
      procedure(dobj_func), pointer :: dobj => null() !! gradient of the objective function
      procedure(con_func), pointer  :: con  => null() !! constraint function
      procedure(dcon_func), pointer :: dcon => null() !! gradient of the constraint function

      procedure(report_f),pointer :: report => null() !! iteration report function

   contains

      private

      procedure, public :: psqpn
      procedure, public :: psqp

      procedure :: compute_obj_and_dobj
      procedure :: dual_range_space_quad_prog
      procedure :: ops_after_constr_deletion
      procedure :: compute_con_and_dcon
      procedure :: extended_line_search

   end type psqp_class