*------------------------------------------------------------
* December 30, 1997
* Wong 2 problem        
*            
* Hock & Schittkowski, 
* Test Examples for Nonlinear Programming Codes.
* Springer-Verlag, 1981.
* Problem 113, page 122.
*
* 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,'Wong 2 Problem')
	write(1,14)
14	format(5x,'Hock & Schittkowski, Problem 113, Page 122.')
*
* Dimension of the problem:
*
	n=10		! No. of variables.
	m=8		! No. of inequality constraints.
	me=0		! No. of equality constraints.
	mb=2*n		! No. of simple bounds on variables.
	nszc=32		! No. of non-zeros in Jacobian of c(x)>=0.
	nsze=0		! No. of non-zeros in Jacobian of e(x) =0.

*
* Initial point:
*
	x(1)=2.d0
	x(2)=3.d0
	x(3)=5.d0
	x(4)=5.d0
	x(5)=1.d0
	x(6)=2.d0
	x(7)=7.d0
	x(8)=3.d0
	x(9)=6.d0
	x(10)=10.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
*
*
* Starting address of columns of the Jacobian of the Equalities
*
*
* Rows indices of the nonzeros of the Jacobian of the INEqualities
*
	icgc(1)=1
	icgc(2)=2
	icgc(3)=3
	icgc(4)=4
	icgc(5)=5
	icgc(6)=6
	icgc(7)=7
	icgc(8)=8
c2
	icgc(9)=1
	icgc(10)=2
	icgc(11)=3
	icgc(12)=4
	icgc(13)=5
	icgc(14)=6
	icgc(15)=7
	icgc(16)=8
c3
	icgc(17)=1
	icgc(18)=2
c4
	icgc(19)=1
	icgc(20)=2
c5
	icgc(21)=3
	icgc(22)=4
c6
	icgc(23)=3
	icgc(24)=4
c7
	icgc(25)=5
	icgc(26)=6
c8
	icgc(27)=5
	icgc(28)=6
c9
	icgc(29)=7
	icgc(30)=8
c10
	icgc(31)=7
	icgc(32)=8
*
* Starting address of columns of the Jacobian of the INEqualities
*
	ipgc(1)=1
	ipgc(2)=9
	ipgc(3)=17
	ipgc(4)=19
	ipgc(5)=21
	ipgc(6)=23
	ipgc(7)=25
	ipgc(8)=27
	ipgc(9)=29
	ipgc(10)=31
	ipgc(11)=33
*
	return
	end
	

*--------------------------------------------------------------
* December 30, 1997
* Wong 2 Problem.
* Hock & Schittkowski, Problem 113, Page 122.
*--------------------------------------------------------------
*
	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)**2 + x(2)**2 + x(1)*x(2) -
     1		14.d0*x(1) - 16.d0*x(2) + 
     1		(x(3)-10.d0)**2 + 4.d0*(x(4)-5.d0)**2 +
     1		(x(5)-3.d0)**2  + 2.d0*(x(6)-1.d0)**2 + 
     1		5.d0*x(7)**2 +
     1		7.d0*(x(8)-11.d0)**2 + 2.d0*(x(9)-10.d0)**2 +
     1		(x(10)-7.d0)**2 + 45.d0
*
	gobj(1)=  2.d0*x(1) + x(2) - 14.d0
	gobj(2)=  2.d0*x(2) + x(1) - 16.d0
	gobj(3)=  2.d0*(x(3)-10.d0)
	gobj(4)=  8.d0*(x(4)-5.d0)
	gobj(5)=  2.d0*(x(5)-3.d0)
	gobj(6)=  4.d0*(x(6)-1.d0)
	gobj(7)= 10.d0*x(7)
	gobj(8)= 14.d0*(x(8)-11.d0)
	gobj(9)=  4.d0*(x(9)-10.d0)
	gobj(10)= 2.d0*(x(10)-7.d0)
*
* Bounds on variables:
*
	j=1
	do i=1,n
	  cb(j)=x(i)+1.d38
	  cb(j+1)=1.d38-x(i)
	  j=j+2
	end do
*
* Constraints. (Inequalities):
*
	c(1)=	-3.d0*(x(1)-2.d0)**2 - 4.d0*(x(2)-3.d0)**2 -
     1		 2.d0*x(3)**2 + 7.d0*x(4) + 120.d0

	c(2)=	-5.d0*x(1)**2 - 8.d0*x(2) - 
     1		 (x(3)-6.d0)**2 + 2.d0*x(4) + 40.d0

	c(3)=	-0.5d0*(x(1)-8.d0)**2 - 2.d0*(x(2)-4.d0)**2 -
     1		 3.d0*x(5)**2 + x(6) + 30.d0

	c(4)=	-x(1)**2 - 2.d0*(x(2)-2.d0)**2 +
     1		 2.d0*x(1)*x(2) - 14.d0*x(5) + 6.d0*x(6)

	c(5)=	-4.d0*x(1) - 5.d0*x(2) + 3.d0*x(7) - 
     1		 9.d0*x(8) + 105.d0

	c(6)=	-10.d0*x(1) + 8.d0*x(2) + 17.d0*x(7) - 2.d0*x(8)

	c(7)=	 3.d0*x(1) - 6.d0*x(2) - 
     1		 12.d0*(x(9)-8.d0)**2 + 7.d0*x(10)

	c(8)=	 8.d0*x(1) - 2.d0*x(2) - 5.d0*x(9) + 
     1		 2.d0*x(10) + 12.d0
*
* Jacobian of the inequalities constraints:
*
	gc(1)=	-6.d0*(x(1)-2.d0)
	gc(2)=	-10.d0*x(1)
	gc(3)=	-(x(1)-8.d0)
	gc(4)=	-2.d0*x(1)
	gc(5)=	-4.d0
	gc(6)=	-10.d0
	gc(7)=	3.d0
	gc(8)=	8.d0
c2
	gc(9)=-8.d0*(x(2)-3.d0)
	gc(10)=-8.d0
	gc(11)=-4.d0*(x(2)-4.d0)
	gc(12)=-4.d0*(x(2)-2.d0)
	gc(13)=-5.d0
	gc(14)=8.d0
	gc(15)=-6.d0
	gc(16)=-2.d0
c3
	gc(17)=-4.d0*x(3)
	gc(18)=-2.d0*(x(3)-6.d0)
c4
	gc(19)=7.d0
	gc(20)=2.d0
c5
	gc(21)=-6.d0*x(5)
	gc(22)=-14.d0
c6
	gc(23)=1.d0
	gc(24)=6.d0
c7
	gc(25)=3.d0
	gc(26)=17.d0
c8
	gc(27)=-9.d0
	gc(28)=-2.d0
c9
	gc(29)=-24.d0*(x(9)-8.d0)
	gc(30)=-5.d0
c10
	gc(31)=7.d0
	gc(32)=2.d0
*
* Constraints. (Equalities):
*
* Jacobian of the equalities constraints:
*
	return
	end
*------------------------------------------------------ HS113.for