*-------------------------------------------------------------
* Date created: October 10, 1996.
* Generated in: Bayreuth University, Mathematics Department
* Prof. Klaus Schittkowski                                 \
*
* Hock & Schittkowski, 
* Test Examples for Nonlinear Programming.
* Springer-Verlag, 1981.
* Problem No. 100.  Page 111.
*
* 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,'Hock-Schittkowski, page 111')
	write(1,14)
14	format(5x,'Problem 100')
*
* Dimension of the problem:
*
	n=7		! No. of variables.
	m=4		! No. of inequality constraints.
	me=0		! No. of equality constraints.
	mb=0		! No. of simple bounds on variables.
	nszc=19		! 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) = 1.d0
	x(2) = 2.d0
	x(3) = 0.d0
	x(4) = 4.d0
	x(5) = 0.d0
	x(6) = 1.d0
	x(7) = 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 Inequalities
*
	icgc(1)=1
	icgc(2)=2
	icgc(3)=3
	icgc(4)=4

	icgc(5)=1
	icgc(6)=2
	icgc(7)=3
	icgc(8)=4

	icgc(9)=1
	icgc(10)=2
	icgc(11)=4

	icgc(12)=1
	icgc(13)=2

	icgc(14)=1
	icgc(15)=2

	icgc(16)=3
	icgc(17)=4

	icgc(18)=3
	icgc(19)=4
*
* Starting address of columns of the Jacobian of the Inequalities
*
	ipgc(1)=1
	ipgc(2)=5
	ipgc(3)=9
	ipgc(4)=12
	ipgc(5)=14
	ipgc(6)=16
	ipgc(7)=18
	ipgc(8)=20
*
* Rows indices of the nonzeros of the Jacobian of the Equalities
*
*
* Starting address of columns of the Jacobian of the Equalities
*
*
*
	return
	end
*

*--------------------------------------------------------------
* Date created: October 10, 1996
* Date modified: October 25, 1996
*
* Problem 100. 
* Hock - Schittkowski, pp.111.
*--------------------------------------------------------------
*
	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)-10.d0)**2 + 5.d0*(x(2)-12.d0)**2 + x(3)**4 +
     1         3.d0*(x(4)-11.d0)**2 + 10.d0*x(5)**6 + 7.d0*x(6)**2 +
     1         x(7)**4 - 4.d0*x(6)*x(7) - 10.d0*x(6) - 8.d0*x(7)

	gobj(1)= 2.d0*(x(1)-10.d0) 
	gobj(2)= 10.d0*(x(2)-12.d0)
	gobj(3)= 4.d0*x(3)**3
	gobj(4)= 6.d0*(x(4)-11.d0)
	gobj(5)= 60.d0*x(5)**5
	gobj(6)= 14.d0*x(6) - 4.d0*x(7) - 10.d0
	gobj(7)= 4.d0*x(7)**3 - 4.d0*x(6) - 8.d0
*
* Bounds on variables:
*
*	j=1
*	do i=1,n
*	   cb(j)=x(i)
*	   cb(j+1)=10.d0-x(i)
*	   j=j+2
*	end do
*
* Constraints. (Inequalities):
*
	c(1)= 127.d0 - 2.d0*x(1)**2 - 3.d0*x(2)**4 - x(3) - 
     1  	4.d0*x(4)**2 - 5.d0*x(5)

	c(2)= 282.d0 - 7.d0*x(1) - 3.d0*x(2) - 10.d0*x(3)**2 - 
     1  	x(4) + x(5)

	c(3)=196.d0 - 23.d0*x(1) - x(2)**2 - 6.d0*x(6)**2 +
     1          8.d0*x(7)

	c(4)=-4.d0*x(1)**2 - x(2)**2 + 3.d0*x(1)*x(2) - 2.d0*x(3)**2 -
     1          5.d0*x(6) + 11.d0*x(7)
*
* Jacobian of the inequalities constraints:
*
	gc(1)= -4.d0*x(1)
	gc(2)= -7.d0
	gc(3)= -23.d0
	gc(4)= -8.d0*x(1) + 3.d0*x(2)

	gc(5)= -12.d0*x(2)**3
	gc(6)= -3.d0
	gc(7)= -2.d0*x(2)
	gc(8)= -2.d0*x(2) + 3.d0*x(1)

	gc(9)= -1.d0
	gc(10)= -20.d0*x(3)
	gc(11)= -4.d0*x(3)

	gc(12)= -8.d0*x(4)
	gc(13)= -1.d0

	gc(14)= -5.d0
	gc(15)=  1.d0

	gc(16)= -12.d0*x(6)
	gc(17)= -5.d0

	gc(18)= 8.d0
	gc(19)= 11.d0
*
* Constraints. (Equalities):
*
* 
* Jacobian of the equalities constraints:
*
*
	return
	end
*------------------------------------------HS100.for