*------------------------------------------------------------
* December 26, 1997
* Brown - Bartholomew-Biggs
* ODE vs SQP methods for constrained optimisation,
* Technical Report No.179, June 1987. 
* The Hatfield Polytechnic, UK.
*
* Problem 12
*
* 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 12, Brown - Bartholomew-Biggs, ')
*
* Dimension of the problem:
*
	n=4     ! 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=4  ! No. of non-zeros in Jacobian of e(x) =0.
*
* Initial point:
*
	x(1)=0.d0
	x(2)=0.d0
	x(3)=-1.d0
	x(4)=-1.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
	icge(3)=1
	icge(4)=1
*
* Starting address of columns of the Jacobian of the equalities
*
	ipge(1)=1
	ipge(2)=2
	ipge(3)=3
	ipge(4)=4
	ipge(5)=5
*
* Rows indices of the nonzeros of the Jacobian of the INEqualities
*
*
* Starting address of columns of the Jacobian of the INEqualities
*
	return
	end
*	
*--------------------------------------------------------------
* BB12     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=	100.d0*(x(2)-x(1)**2)**8 + (1.d0-x(1))**8
*
	gobj(1)=800.d0*((x(2)-x(1)**2)**7)*(-2.d0*x(1)) - 
     1		8.d0*(1.d0-x(1))**7
	gobj(2)=800.d0*(x(2)-x(1)**2)**7
*
* 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)=	100000.d0*(x(2)-x(1)**2)**2 + (1.d0-x(1))**2 +
     1		 90000.d0*(x(4)-x(3)**2)**2 + (1.d0-x(3))**2 +
     1		0.101d0*(x(2)-1.d0)**2 + 0.101d0*(x(4)-1.d0)**2 +
     1		0.198d0*(x(2)-1.d0)*(x(4)-1.d0)
*
* Jacobian of the equalities constraints:
*
	ge(1)=  200000.d0*(x(2)-x(1)**2)*(-2.d0*x(1)) - 
     1		2.d0*(1.d0-x(1))
	ge(2)=  200000.d0*(x(2)-x(1)**2) + 0.202d0*(x(2)-1.d0) +
     1		0.198d0*(x(4)-1.d0)
	ge(3)=  180000.d0*(x(4)-x(3)**2)*(-2.d0*x(3)) -
     1		2.d0*(1.d0-x(3))
	ge(4)=  180000.d0*(x(4)-x(3)**2) + 0.202d0*(x(4)-1.d0) +
     1		0.198d0*(x(2)-1.d0)
*
	return
	end
*----------------------------------------------------BB12.for