*------------------------------------------------------------
* December 26, 1997
* Brown - Bartholomew-Biggs  
* ODE vs SQP methods for constrained optimisation,
* Technical Report No.179, June 1987. 
* The Hatfield Polytechnic, UK.
*
* Problem 13 ("Four-Leaved Rose")
*
* Project: Test Problems with SPENBAR
*
* Dr. Neculai Andrei
* Research Institute for Informatics,
* 8-10, Averescu Avenue, Bucharest 1, Romania
* E-mail: nandrei@u3.ici.ro
* web: www.ici.ro/camo
*------------------------------------------------------------
*
	subroutine ini(n,m,mb,me,sb,x,icgc,ipgc,icge,ipge,
     1                 nszc,nsze,nb)
*

	double precision x(n)
	integer sb(mb)
	integer icgc(nszc),ipgc(n+1)
	integer icge(nsze),ipge(n+1)

*
* Information about the problem.
*
	write(1,10)
10	format(5x,'Example of nonlinear programming.')
	write(1,11)
11	format(5x,'Problem 13, Brown - Bartholomew-Biggs, ')
	write(1,14)
14	format(5x,'Four-Leaved Rose')
*
* Dimension of the problem:
*
	n=2     ! No. of variables.
	m=0     ! No. of inequality constraints.
	me=1    ! No. of equality constraints.
	mb=2*n  ! No. of simple bounds on variables.
	nszc=0  ! No. of non-zeros in Jacobian of c(x)>=0.
	nsze=2  ! No. of non-zeros in Jacobian of e(x) =0.

*
* Initial point:
*
	x(1)=-2.d0
	x(2)= 2.d0
*
* Index vector for simple bounds: cb >= 0.
*
	j=1
	do i=1,n
	   sb(j)=i
	   sb(j+1)=-i
	   j=j+2
	end do
*
* Rows indices of the nonzeros of the Jacobian of the equalities
*
	icge(1)=1
	icge(2)=1
*
* Starting address of columns of the Jacobian of the equalities
*
	ipge(1)=1
	ipge(2)=2
	ipge(3)=3
*
* Rows indices of the nonzeros of the Jacobian of the INEqualities
*
*
* Starting address of columns of the Jacobian of the INEqualities
*
	return
	end
*
*--------------------------------------------------------------
* BB13     Brown - Bartholomew-Bigs
*--------------------------------------------------------------
*
	subroutine prob(n,m,mb,me,sb,x,objf,gobj,c,gc,cb,e,ge,
     1                  nszc,nsze,nb)
*
* Calculate problem function at iterate x.
*
	double precision x(n),objf,gobj(n),c(m),gc(nszc)
	double precision cb(mb),e(me),ge(nsze)
*
*
* Objective function and its gradient:
*
	objf=	-x(1)
*
	gobj(1)=-1.d0
	gobj(2)= 0.d0
*
* Bounds on variables:
*
	j=1
	do i=1,n
	  cb(j)=x(i)+10.d0
	  cb(j+1)=10.d0-x(i)
	  j=j+2
	end do
*
* Constraints. (Inequalities):
*
*
* Jacobian of the inequalities constraints:
*
*
* Constraints. (Equalities):
*
	e(1)=	x(1)**6 + 3.d0*(x(1)**4)*(x(2)**2) +
     1		3.d0*(x(1)**2)*(x(2)**4) + x(2)**6 -
     1		4.d0*x(1)**4 + 8.d0*(x(1)**2)*(x(2)**2) -
     1		4.d0*x(2)**4
*
* Jacobian of the equalities constraints:
*
	ge(1)=	6.d0*x(1)**5 + 12.d0*(x(1)**3)*(x(2)**2) +
     1		6.d0*x(1)*(x(2)**4) - 16.d0*x(1)**3 +
     1		16.d0*x(1)*(x(2)**2)

	ge(2)=	6.d0*(x(1)**4)*x(2) + 12.d0*(x(1)**2)*(x(2)**3) +
     1		6.d0*x(2)**5 + 16.d0*(x(1)**2)*x(2) -
     1		16.d0*(x(2)**3)
*
	return
	end
*----------------------------------------------------BB13.for