* Date created: October 10, 1996.
* Bayreuth University, Mathematics Department
* Problem 106 
* Hock - Schittkowski Page 115.
*
* Heat exchanger design
*
* 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
*
* During my stay in Bayreuth University, Mathematics Department
*--------------------------------------------------------------
*
	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 106, Hock-Schittkowski pp.115')
	write(1,14)
14	format(5x,'')
*
* Dimension of the problem:
*
	n=8		! No. of variables.
	m=6		! No. of inequality constraints.
	me=0		! No. of equality constraints.
	mb=16		! No. of simple bounds on variables.
	nszc=17		! 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) = 5000.d0
	x(2) = 5000.d0
	x(3) = 5000.d0
	x(4) = 200.d0
	x(5) = 350.d0
	x(6) = 150.d0
	x(7) = 225.d0
	x(8) = 425.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)=4

	icgc(2)=5

	icgc(3)=6

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

	icgc(8)=2
	icgc(9)=3
	icgc(10)=5
	icgc(11)=6

	icgc(12)=1
	icgc(13)=4

	icgc(14)=2
	icgc(15)=5

	icgc(16)=3
	icgc(17)=6
*
* Starting address of columns of the Jacobian of the Inequalities
*
	ipgc(1)=1
	ipgc(2)=2
	ipgc(3)=3
	ipgc(4)=4
	ipgc(5)=8
	ipgc(6)=12
	ipgc(7)=14
	ipgc(8)=16
	ipgc(9)=18
*
* 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
* Problem 106. 
* Hock - Schittkowski, pp.115.
*--------------------------------------------------------------
*
	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) + x(2) + x(3) 

	gobj(1)= 1.d0 
	gobj(2)= 1.d0 
	gobj(3)= 1.d0
	gobj(4)= 0.d0
	gobj(5)= 0.d0
	gobj(6)= 0.d0
	gobj(7)= 0.d0 
	gobj(8)= 0.d0
*
* Bounds on variables:
*
	cb(1) = x(1) - 100.d0
	cb(2) = 10000.d0 - x(1)
	cb(3) = x(2) - 1000.d0
	cb(4) = 10000.d0 - x(2)
	cb(5) = x(3) - 1000.d0
	cb(6) = 10000.d0 - x(3)
	j=7
	do i=4,n
	   cb(j)=x(i)-10.d0
	   cb(j+1)=1000.d0-x(i)
	   j=j+2
	end do
*
* Constraints. (Inequalities):
*
	c(1)= 1.d0 - 0.0025d0*(x(4)+x(6))

	c(2)= 1.d0 - 0.0025d0*(x(5)+x(7)-x(4))

	c(3)= 1.d0 - 0.01d0*(x(8)-x(5))

	c(4)= x(1)*x(6) - 833.33252d0*x(4) - 100.d0*x(1) + 83333.333d0

	c(5)= x(2)*x(7) - 1250.d0*x(5) - x(2)*x(4) + 1250.d0*x(4)

	c(6)= x(3)*x(8) - x(3)*x(5) + 2500.d0*x(5) - 1250000.d0
*
* Jacobian of the inequalities constraints:
*
	gc(1)= x(6)-100.d0

	gc(2)= x(7)-x(4)

	gc(3)= x(8)-x(5)

	gc(4)= -0.0025d0 
	gc(5)= 0.0025d0
	gc(6)= -833.33252d0
	gc(7)= -x(2)+1250.d0

	gc(8)= -0.0025d0
	gc(9)= 0.01d0
	gc(10)= -1250.d0
	gc(11)= -x(3)+2500.d0

	gc(12)= -0.0025d0
	gc(13)= x(1)

	gc(14)= -0.0025d0
	gc(15)= x(2)

	gc(16)= -0.01d0
	gc(17)= x(3)
*
* Constraints. (Equalities):
*
* 
* Jacobian of the equalities constraints:
*
*
	return
	end
*-------------------------------------------------HS106.for