*-----------------------------------------------------------
* Date created: June 18, 1996
* Hock & Schittkowski, 
* Test Examples for Nonlinear Programming.
* Springer-Verlag, 1981.
* Problem No. 114.  Page 123.
*
* Alkylation Problem.
*
* 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,'Alkylation Problem, Hock & Schittkowski,')
	write(1,12)
12	format(5x,'Problem 114, Page 123.')
*
* Dimension of the problem:
*
	n=10		! No. of variables.
	m=8		! No. of inequality constraints.
	me=3		! No. of equality constraints.
	mb=20		! No. of simple bounds on variables.
	nszc=20		! No. of non-zeros in Jacobian of c(x)>=0.
	nsze=11		! No. of non-zeros in Jacobian of e(x) =0.

*
* Initial point:
*
	x(1)=1745.d0
	x(2)=12000.d0
	x(3)=110.d0
	x(4)=3048.d0
	x(5)=1974.d0
	x(6)=89.2d0
	x(7)=92.8d0
	x(8)=8.d0
	x(9)=3.6d0
	x(10)=145.1d0
*
* 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)=5
	icgc(2)=7
	icgc(3)=5
	icgc(4)=7
	icgc(5)=6
	icgc(6)=8
	icgc(7)=2
	icgc(8)=4
	icgc(9)=6
	icgc(10)=8
	icgc(11)=5
	icgc(12)=6
	icgc(13)=7
	icgc(14)=8
	icgc(15)=1
	icgc(16)=3
	icgc(17)=1
	icgc(18)=2
	icgc(19)=3
	icgc(20)=4
*
* Starting address of columns of the Jacobian of the Inequalities
*
	ipgc(1)=1
	ipgc(2)=0  ! zero column
	ipgc(3)=0  ! zero column
	ipgc(4)=3
	ipgc(5)=0  ! zero column
	ipgc(6)=5
	ipgc(7)=7
	ipgc(8)=11
	ipgc(9)=15
	ipgc(10)=17
	ipgc(11)=21
*
* Rows indices of the nonzeros of the Jacobian of the Equalities
*
	icge(1)=1	
	icge(2)=3	
	icge(3)=3	
	icge(4)=2	
	icge(5)=1	
	icge(6)=2	
	icge(7)=1	
	icge(8)=3	
	icge(9)=2	
	icge(10)=3	
	icge(11)=2
*	
* Starting address of columns of the Jacobian of the Equalities
*
	ipge(1)=1
	ipge(2)=3
	ipge(3)=4
	ipge(4)=5
	ipge(5)=7
	ipge(6)=9
	ipge(7)=0    ! zero column
	ipge(8)=10
	ipge(9)=11
	ipge(10)=0   ! zero column
	ipge(11)=12
*
	return
	end
*

*--------------------------------------------------------------
* Date created: June 18, 1996
* Hock Schittkowski, No. 114  
* Alkylation Problem.
*--------------------------------------------------------------
*
	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 a,b
*----
* Objective function and its gradient:
*
        objf=5.04d0*x(1)+0.035d0*x(2)+10.d0*x(3)+3.36*x(5)-
     1		0.063d0*x(4)*x(7)
*
	gobj(1)=5.04d0
	gobj(2)=0.035d0
	gobj(3)=10.d0
	gobj(4)=-0.063d0*x(7)
	gobj(5)=3.36d0
	gobj(6)=0.d0
	gobj(7)=-0.063d0*x(4)
	gobj(8)=0.d0
	gobj(9)=0.d0
	gobj(10)=0.d0
*
* Bounds on variables:
*
	cb(1)=x(1)-0.00001d0
	cb(2)=2000.d0-x(1)
	cb(3)=x(2)-0.00001d0
	cb(4)=16000.d0-x(2)
	cb(5)=x(3)-0.00001d0
	cb(6)=120.d0-x(3)
	cb(7)=x(4)-0.00001d0
	cb(8)=5000.d0-x(4)
	cb(9)=x(5)-0.00001d0
	cb(10)=2000.d0-x(5)
	cb(11)=x(6)-85.d0
	cb(12)=93.d0-x(6)
	cb(13)=x(7)-90.d0
	cb(14)=95.d0-x(7)
	cb(15)=x(8)-3.d0
	cb(16)=12.d0-x(8)
	cb(17)=x(9)-1.2d0
	cb(18)=4.d0-x(9)
	cb(19)=x(10)-145.d0
	cb(20)=162.d0-x(10)
*
* Constraints. (Inequalities):
*
	a=0.99d0
	b=0.9d0
*
	c(1)=35.82d0 - 0.222d0*x(10) - 0.9d0*x(9)
	c(2)=-133.d0 + 3.d0*x(7) - 0.99d0*x(10)
	c(3)=-c(1) + (1.d0/b-b)*x(9)
	c(4)=-c(2) + (1.d0/a-a)*x(10)
	c(5)=1.12*x(1) + 0.13167d0*x(1)*x(8) - 
     1	     0.00667d0*x(1)*x(8)*x(8) - a*x(4)
	c(6)=57.425 + 1.098d0*x(8) - 0.038*x(8)*x(8) +
     1	     0.325d0*x(6) - a*x(7)
	c(7)=-c(5) + (1.d0/a-a)*x(4)
	c(8)=-c(6) + (1.d0/a-a)*x(7)
*
* Jacobian of the inequalities constraints:
*
	gc(1)=1.12d0 + 0.13167*x(8) - 0.00667*x(8)*x(8)
	gc(2)=-gc(1)
	gc(3)=-a
	gc(4)=1.d0/a
	gc(5)=0.325d0
	gc(6)=-0.325d0
	gc(7)=3.d0
	gc(8)=-3.d0
	gc(9)=-a
	gc(10)=1.d0/a
	gc(11)=0.13167d0*x(1)-2.d0*0.00667*x(1)*x(8)
	gc(12)=1.098d0-2.d0*0.038*x(8)
	gc(13)=-gc(11)
	gc(14)=-gc(12)
	gc(15)=-b
	gc(16)=1.d0/b
	gc(17)=-0.222d0
	gc(18)=-a
	gc(19)=0.222d0
	gc(20)=1.d0/a
*
* Constraints. (Equalities):
*
	e(1)=1.22d0*x(4) - x(1) - x(5)
	e(2)=98000.d0*x(3)/(x(4)*x(9)+1000.d0*x(3)) - x(6)
	e(3)=(x(2)+x(5))/x(1) - x(8)
*
* Jacobian of the equalities constraints:
*
	ge(1)=-1.d0
	ge(2)=-(x(2)+x(5))/(x(1)*x(1))
	ge(3)=1.d0/x(1)
	ge(4)=98000.d0*x(4)*x(9)/((x(4)*x(9)+1000.d0*x(3))**2)
	ge(5)=1.22d0
	ge(6)=-98000.d0*x(3)*x(9)/((x(4)*x(9)+1000.d0*x(3))**2)
	ge(7)=-1.d0
	ge(8)=1.d0/x(1)
	ge(9)=-1.d0
	ge(10)=-1.d0
	ge(11)=-98000.d0*x(3)*x(4)/((x(4)*x(9)+1000.d0*x(3))**2)
*
	return
	end
*--------------------------------------------------ALKIL.for