C     =================================================================
C     File: problem09.f
C     =================================================================

C     ******************************************************************
C     ******************************************************************

      subroutine inip(n,x,l,u,m,lambda,rho,equatn,linear,ml,meq,alin,
     +acol,aval,annz,b,fknown)

      implicit none

C     SCALAR ARGUMENTS
      integer annz,m,ml,meq,n
      double precision fknown

C     ARRAY ARGUMENTS
      logical equatn(*),linear(*)
      integer alin(*),acol(*)
      double precision aval(*),b(*),l(*),lambda(*),rho(*),u(*),x(*)

C     This subroutine must set some problem data. For achieving this 
C     objective YOU MUST MODIFY it according to your problem. See below 
C     where your modifications must be inserted.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     This subroutine has no input parameters.
C
C     On Return
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              initial point,
C
C     l        double precision l(n),
C              lower bounds on x,
C
C     u        double precision u(n),
C              upper bounds on x,
C
C     m        integer,
C              number of constraints (excluding the bounds),
C
C     lambda   double precision lambda(m),
C              initial estimation of the Lagrange multipliers,
C
C     rho      double precision rho(m),
C              initial penalty parameters.
C
C     equatn   logical equatn(m)
C              for each constraint j, set equatn(j) = .true. if it is an 
C              equality constraint of the form c_j(x) = 0, and set 
C              equatn(j) = .false. if it is an inequality constraint of 
C              the form c_j(x) <= 0,
C
C     linear   logical linear(m)
C              for each constraint j, set linear(j) = .true. if it is a 
C              linear constraint, and set linear(j) = .false. if it is a
C              nonlinear constraint.

C     LOCAL SCALARS
      integer i
      double precision seed

C     EXTERNAL FUNCTIONS
      double precision drand

C     Set problem data
C     write(*,*) 'Seed for the random initial point: '
C     read(*,*) seed
      seed = 123456.0d0

C     Number of variables
      n = 6

C     Lower and upper bounds
      l(1) = 1.0d-05
      l(2) = 1.0d-05
      l(3) = 1.0d-05
      l(4) = 0.0d0
      l(5) = 0.0d0
      l(6) = 0.0d0

      u(1) = 3.0d0
      u(2) = 4.0d0
      u(3) = 4.0d0
      u(4) = 2.0d0
      u(5) = 2.0d0
      u(6) = 6.0d0

C     Initial point
      do i = 1,n
          x(i) = l(i) + ( u(i) - l(i) ) * drand(seed)
      end do

C     Number of constraints (equalities plus inequalities)

      m = 0

C     Set the sparse matrix and the right hand side of the linear
C     constraints of the form ai^t x = bi for i = 1, ..., meq and
C     ai^t x >= bi for i = meq + 1,ml. These linear constraints will
C     be lower-level constraints. All the previous constraints will
C     be upper-lever constraints. The suggestions is to consider the
C     linear constraints as lower-level constraints, but it is not
C     mandatory.

      ml  = 6
      meq = 3

      annz = 14

C     - 3.0d0 * x(1) + x(2) - 3.0d0 * x(4) = 0 

      alin(1) = 1
      acol(1) = 1
      aval(1) = - 3.0d0

      alin(2) = 1
      acol(2) = 2
      aval(2) =   1.0d0

      alin(3) = 1
      acol(3) = 4
      aval(3) = - 3.0d0

      b(1) = 0.0d0

C     - 2.0d0 * x(2) + x(3) - 2.0d0 * x(5) = 0

      alin(4) = 2
      acol(4) = 2
      aval(4) = - 2.0d0

      alin(5) = 2
      acol(5) = 3
      aval(5) =   1.0d0

      alin(6) = 2
      acol(6) = 5
      aval(6) = - 2.0d0

      b(2) = 0.0d0

C     4.0d0 * x(4) - x(6) = 0

      alin(7) = 3
      acol(7) = 4
      aval(7) =   4.0d0

      alin(8) = 3
      acol(8) = 6
      aval(8) = - 1.0d0

      b(3) = 0.0d0

C     - x(1) - 2.0d0 * x(4) >= - 4.0d0

      alin(9) = 4
      acol(9) = 1
      aval(9) = - 1.0d0

      alin(10) = 4
      acol(10) = 4
      aval(10) = - 2.0d0

      b(4) = - 4.0d0

C     - x(2) - x(5) >= - 4.0d0

      alin(11) = 5
      acol(11) = 2
      aval(11) = - 1.0d0

      alin(12) = 5
      acol(12) = 5
      aval(12) = - 1.0d0

      b(5) = - 4.0d0

C     - x(3) - x(6) >= - 6.0d0

      alin(13) = 6
      acol(13) = 3
      aval(13) = - 1.0d0

      alin(14) = 6
      acol(14) = 6
      aval(14) = - 1.0d0

      b(6) = - 6.0d0

      fknown = -1.340190355505064d+01

      end

C     ******************************************************************
C     ******************************************************************

      subroutine evalf(n,x,f,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,n
      double precision f

C     ARRAY ARGUMENTS
      double precision x(n)

C     This subroutine must compute the objective function. For achieving 
C     this objective YOU MUST MODIFY it according to your problem. See 
C     below where your modifications must be inserted.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     On Return
C
C     f        double precision,
C              objective function value at x,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the objective 
C              function. (For example, trying to compute the square root 
C              of a negative number, dividing by zero or a very small 
C              number, etc.) If everything was o.k. you must set it 
C              equal to zero.

      flag = 0

      f = x(1) ** 0.6d0 + x(2) ** 0.6d0 + x(3) ** 0.4d0 - 4.0d0 * x(3)
     +  + 2.0d0 * x(4) + 5.0d0 * x(5) - x(6)

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalg(n,x,g,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,n

C     ARRAY ARGUMENTS
      double precision g(n),x(n)

C     This subroutine must compute the gradient vector of the objective 
C     function. For achieving these objective YOU MUST MODIFY it in the 
C     way specified below. However, if you decide to use numerical 
C     derivatives (we dont encourage this option at all!) you dont need
C     to modify evalg.
C
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     On Return
C
C     g        double precision g(n),
C              gradient vector of the objective function evaluated at x,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of any component 
C              of the gradient vector. (For example, trying to compute 
C              the square root of a negative number, dividing by zero or 
C              a very small number, etc.) If everything was o.k. you 
C              must set it equal to zero.

      flag = 0

      g(1) = 0.6d0 * x(1) ** ( - 0.4d0 )
      g(2) = 0.6d0 * x(2) ** ( - 0.4d0 )
      g(3) = 0.4d0 * x(3) ** ( - 0.6d0 ) - 4.0d0
      g(4) = 2.0d0
      g(5) = 5.0d0
      g(6) = - 1.0d0

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalh(n,x,hlin,hcol,hval,hnnz,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,n,hnnz

C     ARRAY ARGUMENTS
      integer hcol(*),hlin(*)
      double precision hval(*),x(n)

C     This subroutine might compute the Hessian matrix of the objective 
C     function. For achieving this objective YOU MAY MODIFY it according 
C     to your problem. To modify this subroutine IS NOT MANDATORY. See 
C     below where your modifications must be inserted.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     On Return
C
C     hnnz     integer,
C              number of perhaps-non-null elements of the computed 
C              Hessian,
C
C     hlin     integer hlin(hnnz),
C              see below,
C
C     hcol     integer hcol(hnnz),
C              see below,
C
C     hval     double precision hval(hnnz),
C              the non-null value of the (hlin(k),hcol(k)) position 
C              of the Hessian matrix of the objective function must 
C              be saved at hval(k). Just the lower triangular part of
C              Hessian matrix must be computed,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the Hessian
C              matrix of the objective funtion. (For example, trying 
C              to compute the square root of a negative number, 
C              dividing by zero or a very small number, etc.) If 
C              everything was o.k. you must set it equal to zero.

      flag = 0

      hnnz = 3

      hlin(1) = 1
      hcol(1) = 1
      hval(1) = - 0.24d0 * x(1) ** ( - 1.4d0 )

      hlin(2) = 2
      hcol(2) = 2
      hval(2) = - 0.24d0 * x(2) ** ( - 1.4d0 )

      hlin(3) = 3
      hcol(3) = 3
      hval(3) = - 0.24d0 * x(3) ** ( - 1.6d0 )

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalc(n,x,ind,c,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer ind,flag,n
      double precision c

C     ARRAY ARGUMENTS
      double precision x(n)

C     This subroutine must compute the ind-th constraint of your 
C     problem. For achieving this objective YOU MUST MOFIFY it 
C     according to your problem. See below the places where your 
C     modifications must be inserted.
C
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     ind      integer,
C              index of the constraint to be computed,
C
C     On Return
C
C     c        double precision,
C              ind-th constraint evaluated at x,
C
C     flag     integer
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the 
C              constraint. (For example, trying to compute the square 
C              root of a negative number, dividing by zero or a very 
C              small number, etc.) If everything was o.k. you must set 
C              it equal to zero.

      flag = - 1

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evaljac(n,x,ind,indjac,valjac,jcnnz,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,ind,n,jcnnz

C     ARRAY ARGUMENTS
      integer indjac(n)
      double precision x(n),valjac(n)

C     This subroutine must compute the gradient of the constraint ind. 
C     For achieving these objective YOU MUST MODIFY it in the way 
C     specified below.
C
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     ind      integer,
C              index of the constraint whose gradient will be computed,
C
C     On Return
C
C     jcnnz   integer,
C              number of perhaps-non-null elements of the computed 
C              gradient,
C
C     indjac   integer indjac(jcnnz),
C              see below,
C
C     valjac   double precision valjac(jcnnz),
C              the non-null value of the partial derivative of the 
C              ind-th constraint with respect to the indjac(k)-th 
C              variable must be saved at valjac(k).
C
C     flag     integer
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the 
C              constraint. (For example, trying to compute the square 
C              root of a negative number, dividing by zero or a very 
C              small number, etc.) If everything was o.k. you must set 
C              it equal to zero.

      flag = - 1

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalhc(n,x,ind,hclin,hccol,hcval,hcnnz,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,ind,n,hcnnz

C     ARRAY ARGUMENTS
      integer hccol(*),hclin(*)
      double precision hcval(*),x(n)

C     This subroutine might compute the Hessian matrix of the ind-th
C     constraint. For achieving this objective YOU MAY MODIFY it 
C     according to your problem. To modify this subroutine IS NOT 
C     MANDATORY. See below where your modifications must be inserted.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     ind      integer,
C              index of the constraint whose Hessian will be computed,
C
C     On Return
C
C     hcnnz    integer,
C              number of perhaps-non-null elements of the computed 
C              Hessian,
C
C     hclin    integer hclin(hcnnz),
C              see below,
C
C     hccol    integer hccol(hcnnz),
C              see below,
C
C     hcval    double precision hcval(hcnnz),
C              the non-null value of the (hclin(k),hccol(k)) position 
C              of the Hessian matrix of the ind-th constraint must 
C              be saved at hcval(k). Just the lower triangular part of
C              Hessian matrix must be computed,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the Hessian
C              matrix of the ind-th constraint. (For example, trying 
C              to compute the square root of a negative number, 
C              dividing by zero or a very small number, etc.) If 
C              everything was o.k. you must set it equal to zero.

      flag = - 1

      end

C     ******************************************************************
C     ******************************************************************

      subroutine evalhlp(n,x,m,lambda,p,hp,goth,flag)

      implicit none

C     SCALAR ARGUMENTS
      logical goth
      integer flag,m,n

C     ARRAY ARGUMENTS
      double precision hp(n),lambda(m),p(n),x(n)

C     This subroutine might compute the product of the Hessian of the
C     Lagrangian times vector p (just the Hessian of the objective 
C     function in the unconstrained or bound-constrained case). 
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     m        integer,
C              number of constraints,
C
C     lambda   double precision lambda(m),
C              vector of Lagrange multipliers,
C
C     p        double precision p(n),
C              vector of the matrix-vector product,
C
C     goth     logical,
C              can be used to indicate if the Hessian matrices were
C              computed at the current point. It is set to .false.
C              by the optimization method every time the current
C              point is modified. Sugestion: if its value is .false. 
C              then compute the Hessians, save them in a common 
C              structure and set goth to .true.. Otherwise, just use 
C              the Hessians saved in the common block structure,
C
C     On Return
C
C     hp       double precision hp(n),
C              Hessian-vector product,
C
C     goth     logical,
C              see above,
C              
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the 
C              Hessian-vector product. (For example, trying to compute 
C              the square root of a negative number, dividing by zero 
C              or a very small number, etc.) If everything was o.k. you 
C              must set it equal to zero.

      flag = - 1

      end

C     ******************************************************************
C     ******************************************************************

      subroutine endp(n,x,l,u,m,lambda,rho,equatn,linear)

      implicit none

C     SCALAR ARGUMENTS
      integer m,n

C     ARRAY ARGUMENTS
      logical equatn(m),linear(m)
      double precision l(n),lambda(m),rho(m),u(n),x(n)

C     This subroutine can be used to do some extra job after the solver
C     has found the solution,like some extra statistics, or to save the
C     solution in some special format or to draw some graphical
C     representation of the solution. If the information given by the
C     solver is enough for you then leave the body of this subroutine
C     empty.
C     
C     Parameters of the subroutine:
C
C     The paraemters of this subroutine are the same parameters of
C     subroutine inip. But in this subroutine there are not output
C     parameter. All the parameters are input parameters.

      end

C     ******************************************************************
C     ******************************************************************

      subroutine addc(n,l,u,f,ml,meq,alin,acol,aval,annz,b,fknown,mla,
     +annza,ind)

C     SCALAR ARGUMENTS
      integer annz,annza,meq,ml,mla,n
      double precision f,fknown

C     ARRAY ARGUMENTS
      integer alin(annz),acol(annz),ind(ml)
      double precision aval(annz),b(ml),l(n),u(n)

C     LOCAL SCALARS
      double precision tmp1,tmp2,tmp3,tmpl1,tmpl2,tmpl3,tmpu1,tmpu2,
     +        tmpu3

      mla   = ml
      annza = annz

C     x(1) ** 0.6d0 + x(2) ** 0.6d0 + x(3) ** 0.4d0 - 4.0d0 * x(3) +
C     2.0d0 * x(4) + 5.0d0 * x(5) - x(6) - f <= 0

C     Linear terms as they are plus linear understimation of 
C     concave terms.

      tmpl1 = l(1) ** 0.6d0
      tmpu1 = u(1) ** 0.6d0
      tmpl2 = l(2) ** 0.6d0
      tmpu2 = u(2) ** 0.6d0
      tmpl3 = l(3) ** 0.4d0
      tmpu3 = u(3) ** 0.4d0

      tmp1 = ( tmpu1 - tmpl1 ) / ( u(1) - l(1) )
      tmp2 = ( tmpu2 - tmpl2 ) / ( u(2) - l(2) )
      tmp3 = ( tmpu3 - tmpl3 ) / ( u(3) - l(3) )

C     Linear underestimators of the concave terms:
C     tmpl1 + tmp1 * ( x(1) - l(1) ) <= x(1) ** 0.6d0
C     tmpl2 + tmp2 * ( x(2) - l(2) ) <= x(2) ** 0.6d0
C     tmpl3 + tmp3 * ( x(3) - l(3) ) <= x(3) ** 0.4d0

      ind(mla+1) = 0

      alin(annza+1) = mla + 1
      acol(annza+1) = 1
      aval(annza+1) = - tmp1

      alin(annza+2) = mla + 1
      acol(annza+2) = 2
      aval(annza+2) = - tmp2

      alin(annza+3) = mla + 1
      acol(annza+3) = 3
      aval(annza+3) = - tmp3 + 4.0d0

      alin(annza+4) = mla + 1
      acol(annza+4) = 4
      aval(annza+4) = - 2.0d0

      alin(annza+5) = mla + 1
      acol(annza+5) = 5
      aval(annza+5) = - 5.0d0

      alin(annza+6) = mla + 1
      acol(annza+6) = 6
      aval(annza+6) = 1.0d0

      b(mla+1) = tmpl1 - tmp1 * l(1) + tmpl2 - tmp2 * l(2) + 
     +           tmpl3 - tmp3 * l(3) - min( f, fknown )

      mla   = mla   + 1
      annza = annza + 6

      end

C     ******************************************************************
C     ******************************************************************

      subroutine setlv(n,linvar)

      implicit none

C     SCALAR ARGUMENTS
      integer n

C     ARRAY ARGUMENTS
      logical linvar(n)

C     LOCAL SCALARS
      integer i

      do i = 1,n
          linvar(i) = .false.
      end do

      linvar(4) = .true.
      linvar(5) = .true.
      linvar(6) = .true.

      end

C     ******************************************************************
C     ******************************************************************

      subroutine evalfi(n,y,f,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,n
      double precision f(2)

C     ARRAY ARGUMENTS
      double precision y(2*n)

C     This subroutine computes the intervalar objective function.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     y        double precision y(2*n),
C              bounds on x variables, y(2*i-1) <= x(i) <= y(2*i),
C
C     On Return
C
C     f        double precision,
C              objective function value at x,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the objective 
C              function. (For example, trying to compute the square root 
C              of a negative number, dividing by zero or a very small 
C              number, etc.) If everything was o.k. you must set it 
C              equal to zero.

C     LOCAL ARRAYS
      double precision tmp(2),tmppow(2)

C     EXTERNAL FUNCTIONS
      integer P

      flag = 0

C     f = x(1) ** 0.6d0 + x(2) ** 0.6d0 + x(3) ** 0.4d0 - 4.0d0 * x(3)
C    +  + 2.0d0 * x(4) + 5.0d0 * x(5) - x(6)

      call ivl1(0.6d0,tmppow)
      call iipowr(y(P(1)),tmppow,f)
      call iipowr(y(P(2)),tmppow,tmp)
      call add(f,tmp,f)
      call ivl1(0.4d0,tmppow)
      call iipowr(y(P(3)),tmppow,tmp)
      call add(f,tmp,f)
      call sclmlt(-4.0d0,y(P(3)),tmp)
      call add(f,tmp,f)
      call sclmlt(2.0d0,y(P(4)),tmp)
      call add(f,tmp,f)
      call sclmlt(5.0d0,y(P(5)),tmp)
      call add(f,tmp,f)
      call sub(f,y(P(6)),f)

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalhi(n,y,hlin,hcol,hval,hnnz,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,n,hnnz

C     ARRAY ARGUMENTS
      integer hcol(*),hlin(*)
      double precision hval(*),y(2*n)

C     This subroutine computes the intervalar Hessian matrix of the 
C     objective function.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     y        double precision y(2*n),
C              bounds on x variables, y(2*i-1) <= x(i) <= y(2*i),
C
C     On Return
C
C     hnnz     integer,
C              number of perhaps-non-null elements of the computed 
C              Hessian,
C
C     hlin     integer hlin(hnnz),
C              see below,
C
C     hcol     integer hcol(hnnz),
C              see below,
C
C     hval     double precision hval(hnnz),
C              the interval of the non-null value of the (hlin(k),hcol(k)) 
C              position of the Hessian matrix of the objective function must 
C              be saved at hval(P(k)). Just the lower triangular part of 
c              Hessian matrix must be computed,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the Hessian
C              matrix of the objective funtion. (For example, trying 
C              to compute the square root of a negative number, 
C              dividing by zero or a very small number, etc.) If 
C              everything was o.k. you must set it equal to zero.

C     LOCAL ARRAYS
      double precision tmppow(2)

C     EXTERNAL FUNCTION
      integer P

      flag = 0

      hnnz = 3

      hlin(1) = 1
      hcol(1) = 1
C     hval(1) = - 0.24d0 * x(1) ** ( - 1.4d0 )
      call ivl1(-1.4d0,tmppow)
      call iipowr(y(P(1)),tmppow,hval(P(1)))
      call sclmlt(-0.24d0,hval(P(1)),hval(P(1)))

      hlin(2) = 2
      hcol(2) = 2
C     hval(2) = - 0.24d0 * x(2) ** ( - 1.4d0 )
      call ivl1(-1.4d0,tmppow)
      call iipowr(y(P(2)),tmppow,hval(P(2)))
      call sclmlt(-0.24d0,hval(P(2)),hval(P(2)))

      hlin(3) = 3
      hcol(3) = 3
C     hval(3) = - 0.24d0 * x(3) ** ( - 1.6d0 )
      call ivl1(-1.6d0,tmppow)
      call iipowr(y(P(3)),tmppow,hval(P(3)))
      call sclmlt(-0.24d0,hval(P(3)),hval(P(3)))

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalci(n,y,ind,c,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer ind,flag,n
      double precision c(2)

C     ARRAY ARGUMENTS
      double precision y(2*n)

C     This subroutine computes the interval of the ind-th constraint of 
C     your problem. 
C
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     y        double precision y(2*n),
C              bounds on x variables, y(2*i-1) <= x(i) <= y(2*i),
C
C     ind      integer,
C              index of the constraint to be computed,
C
C     On Return
C
C     c        double precision,
C              interval of the ind-th constraint "evaluated at y",
C
C     flag     integer
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the 
C              constraint. (For example, trying to compute the square 
C              root of a negative number, dividing by zero or a very 
C              small number, etc.) If everything was o.k. you must set 
C              it equal to zero.

      flag = - 1

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evaljaci(n,y,ind,indjac,valjac,jcnnz,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,ind,n,jcnnz

C     ARRAY ARGUMENTS
      integer indjac(n)
      double precision y(2*n),valjac(2*n)

C     This subroutine must compute the intervalar gradient of the 
C     constraint ind. 
C
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     y        double precision y(2*n),
C              bounds on x variables, y(2*i-1) <= x(i) <= y(2*i),
C
C     ind      integer,
C              index of the constraint whose intervalar gradient will be 
C              computed,
C
C     On Return
C
C     jcnnz   integer,
C              number of perhaps-non-null elements of the computed 
C              gradient,
C
C     indjac   integer indjac(jcnnz),
C              see below,
C
C     valjac   double precision valjac(jcnnz),
C              the interval of the non-null value of the partial 
C              derivative of the ind-th constraint with respect to the 
C              indjac(k)-th variable must be saved at valjac(P(k)).
C
C     flag     integer
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the 
C              constraint. (For example, trying to compute the square 
C              root of a negative number, dividing by zero or a very 
C              small number, etc.) If everything was o.k. you must set 
C              it equal to zero.

      flag = - 1

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalhci(n,y,ind,hclin,hccol,hcval,hcnnz,flag)

      implicit none

C     SCALAR ARGUMENTS
      integer flag,ind,n,hcnnz

C     ARRAY ARGUMENTS
      integer hccol(*),hclin(*)
      double precision hcval(*),y(2*n)

C     This subroutine might compute the intervalar Hessian matrix of 
C     the ind-th constraint. 
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     y        double precision y(2*n),
C              bounds on x variables, y(2*i-1) <= x(i) <= y(2*i),
C
C     ind      integer,
C              index of the constraint whose Hessian will be computed,
C
C     On Return
C
C     hcnnz    integer,
C              number of perhaps-non-null elements of the computed 
C              Hessian,
C
C     hclin    integer hclin(hcnnz),
C              see below,
C
C     hccol    integer hccol(hcnnz),
C              see below,
C
C     hcval    double precision hcval(hcnnz),
C              the interval of the non-null value of the (hclin(k),hccol(k)) 
C              position of the Hessian matrix of the ind-th constraint must 
C              be saved at hcval(P(k)). Just the lower triangular part of 
C              Hessian matrix must be computed,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the Hessian
C              matrix of the ind-th constraint. (For example, trying 
C              to compute the square root of a negative number, 
C              dividing by zero or a very small number, etc.) If 
C              everything was o.k. you must set it equal to zero.

      flag = - 1

      end