* Date created: April 11, 1997   
*
* Neculai Andrei,
* Advanced Mathematical Programming. Theory,
* Computational Methods, Applications.
* Technical Press, Bucharest, 1999.
*
* Problem N8, pp.800.
*
* Dr. Neculai Andrei,
* Research Institute for Informatics - Bucharest
* 8-10, Averescu Avenue,
* 71316 Bucharest - Romania      
* E-mail: nandrei@u3.ici.ro    
* web: http://www.ici.ro/camo/neculai/nandrei.htm
*-----------------------------------------------------------
*
	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 N8. Andrei, AMP, 1999')
*
* Dimension of the problem:
*
	n=10		! No. of variables.
	m=0		! No. of inequality constraints.
	me=5		! 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=30		! No. of non-zeros in Jacobian of e(x) =0.

*
* Initial point:
*
	x(1)=-2.d0
	x(2)=-1.d0/2.d0
	x(3)=3.d0
	x(4)=1.d0/3.d0
	x(5)=-4.d0
	x(6)=-1.d0/4.d0
	x(7)=5.d0
	x(8)=1.d0/5.d0
	x(9)=-6.d0
	x(10)=-1.d0/6.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 Inequalities
*
* Starting address of columns of the Jacobian of the Inequalities
*
* Rows indices of the nonzeros of the Jacobian of the Equalities
*
	icge(1)=1	
	icge(2)=2
	icge(3)=3	
	icge(4)=4	
	icge(5)=5	
	icge(6)=1	
	icge(7)=2	
	icge(8)=3
	icge(9)=4
	icge(10)=5
	icge(11)=2
	icge(12)=3	
	icge(13)=4	
	icge(14)=5	
	icge(15)=2	
	icge(16)=3
	icge(17)=4	
	icge(18)=5
	icge(19)=3
	icge(20)=4	
	icge(21)=5	
	icge(22)=3	
	icge(23)=4	
	icge(24)=5	
	icge(25)=4	
	icge(26)=5	
	icge(27)=4
	icge(28)=5
	icge(29)=5	
	icge(30)=5
*	
* Starting address of columns of the Jacobian of the Equalities
*
	ipge(1)=1
	ipge(2)=6
	ipge(3)=11
	ipge(4)=15
	ipge(5)=19
	ipge(6)=22
	ipge(7)=25
	ipge(8)=27
	ipge(9)=29
	ipge(10)=30
	ipge(11)=31
*
	return
	end
*

*--------------------------------------------------------------
* Date created: April 11, 1997
* N8 Test Problem   (Advanced Mathematical Programming, pp.800)
*--------------------------------------------------------------
*
	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)

	real*8 t(5)
*
* Objective function and its gradient:
*
        objf=   (x(1)-x(2))**2 + (x(2)-x(3))**2 +
     1		(x(3)-x(4))**2 + (x(4)-x(5))**2 +
     1		(x(5)-x(6))**2 + (x(6)-x(7))**2 +
     1		(x(7)-x(8))**2 + (x(8)-x(9))**2 +
     1		(x(9)-x(10))**2
*
	gobj(1)=  2.d0*(x(1)-x(2))
	gobj(2)= -2.d0*(x(1)-x(2)) + 2.d0*(x(2)-x(3))
	gobj(3)= -2.d0*(x(2)-x(3)) + 2.d0*(x(3)-x(4))
	gobj(4)= -2.d0*(x(3)-x(4)) + 2.d0*(x(4)-x(5))
	gobj(5)= -2.d0*(x(4)-x(5)) + 2.d0*(x(5)-x(6))
	gobj(6)= -2.d0*(x(5)-x(6)) + 2.d0*(x(6)-x(7))
	gobj(7)= -2.d0*(x(6)-x(7)) + 2.d0*(x(7)-x(8))
	gobj(8)= -2.d0*(x(7)-x(8)) + 2.d0*(x(8)-x(9))
	gobj(9)= -2.d0*(x(8)-x(9)) + 2.d0*(x(9)-x(10))
	gobj(10)=-2.d0*(x(9)-x(10))
*
* Bounds on variables:
*
	j=1
	do i=1,n
	  cb(j)=x(i)+1000.d0
	  cb(j+1)=1000.d0-x(i)
	  j=j+2
	end do
*
* Constraints. (Inequalities):
*
*
* Jacobian of the inequalities constraints:
*
* Constraints. (Equalities):
*
	t(1)=     x(1)*x(2)  
	t(2)=t(1)*x(3)*x(4)  
	t(3)=t(2)*x(5)*x(6)  
	t(4)=t(3)*x(7)*x(8)  
	t(5)=t(4)*x(9)*x(10) 

	e(1) = t(1) - 1.d0
	e(2) = t(2) - 1.d0
	e(3) = t(3) - 1.d0
	e(4) = t(4) - 1.d0
	e(5) = t(5) - 1.d0
*
* Jacobian of the equalities constraints:
*
c1
	ge(1)=x(2)
	ge(2)=ge(1)*x(3)*x(4)
	ge(3)=ge(2)*x(5)*x(6)
	ge(4)=ge(3)*x(7)*x(8)
	ge(5)=ge(4)*x(9)*x(10)
c2
	ge(6)=x(1)
	ge(7)=ge(6)*x(3)*x(4)
	ge(8)=ge(7)*x(5)*x(6)
	ge(9)=ge(8)*x(7)*x(8)
	ge(10)=ge(9)*x(9)*x(10)
c3
	ge(11)=x(1)*x(2)*x(4)
	ge(12)=ge(11)*x(5)*x(6)
	ge(13)=ge(12)*x(7)*x(8)
	ge(14)=ge(13)*x(9)*x(10)
c4
	ge(15)=x(1)*x(2)*x(3)
	ge(16)=ge(15)*x(5)*x(6)
	ge(17)=ge(16)*x(7)*x(8)
	ge(18)=ge(17)*x(9)*x(10)
c5
	ge(19)=x(1)*x(2)*x(3)*x(4)*x(6)
	ge(20)=ge(19)*x(7)*x(8)
	ge(21)=ge(20)*x(9)*x(10)
c6
	ge(22)=x(1)*x(2)*x(3)*x(4)*x(5)
	ge(23)=ge(22)*x(7)*x(8)
	ge(24)=ge(23)*x(9)*x(10)
c7
	ge(25)=x(1)*x(2)*x(3)*x(4)*x(5)*x(6)*x(8)
	ge(26)=ge(25)*x(9)*x(10)
c8
	ge(27)=x(1)*x(2)*x(3)*x(4)*x(5)*x(6)*x(7)
	ge(28)=ge(27)*x(9)*x(10)
c9
	ge(29)=x(1)*x(2)*x(3)*x(4)*x(5)*x(6)*x(7)*x(8)*x(10)
c10
	ge(30)=x(1)*x(2)*x(3)*x(4)*x(5)*x(6)*x(7)*x(8)*x(9)
*
	return
	end                                                
*	
*---------------------------------------------------AMPN8.for