*---------------------------------------------------------
* Date created:  December 23, 1997
* 
* Hock, W., Schittkowski, K., 
* Test examples for nonlinear programming codes.
* Springer-Verlag, 1981.
* Problem 112, pp,121   
*
* Chemical equilibrium
*
* 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)
*
	write(1,10)
10	format(5x,'Example of a Nonlinear Programming Problem.')
	write(1,11)
11	format(5x,'Schittkowski, prob 112, pp.121')     
        write(1,12)
12      format(5x,'Chemical Equilibrium')        
*
      n=10
      m=0
      me=3
      mb=2*n
      nszc=0
      nsze=14
*
* Initial Point
*
	do i=1,n
	  x(i)=0.1d0
	end do
*
* Index vector for simple bounds:
*
      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.
*
	icge(1)=1
	icge(2)=1
	icge(3)=1
	icge(4)=3
	icge(5)=2
	icge(6)=2
	icge(7)=1
	icge(8)=2
	icge(9)=2
	icge(10)=3
	icge(11)=3
	icge(12)=3
	icge(13)=1
	icge(14)=3
*
* Starting address of the columns of the Jacobian of the Equalities.
*
	ipge(1)=1
	ipge(2)=2
	ipge(3)=3
	ipge(4)=5
	ipge(5)=6
	ipge(6)=7
	ipge(7)=9
	ipge(8)=11
	ipge(9)=12
	ipge(10)=13
	ipge(11)=15
*
* Rows indices of the nonzeros of the Jacobian of the INEqualities.
*
*
* Starting address of the columns of the Jacobian of the INEqualities.
*
*
      return
      end
*

*--------------------------------------------------------------
* Date created:  December 23, 1997
* Hock & Schittkowski, prob. 112, pp.121. (Chemical Equilibrium)
*--------------------------------------------------------------
*
      subroutine prob(n,m,mb,me,sb,x,objf,gobj,c,gc,cb,e,ge,
     1                nszc,nsze,nb)
*
* Calculate problem functions at iterate x.
*
      double precision x(n),objf,gobj(n),c(m),gc(nszc),
     *   cb(mb),e(me),ge(nsze)
      real*8 c1(10), t
*
* Objective function, and its gradient.
*
	c1(1)=-6.089d0
	c1(2)=-17.164d0
	c1(3)=-34.054d0
	c1(4)=-5.914d0
	c1(5)=-24.721d0
	c1(6)=-14.986d0
	c1(7)=-24.100d0
	c1(8)=-10.708d0
	c1(9)=-26.662d0
	c1(10)=-22.179d0
*
	objf=0.d0

	   t=0.d0
	   do i=1,n
	      t=t+x(i)
	   end do

	do j=1,n
	  objf = objf + x(j)*( c1(j) + dlog(x(j)/t) )
	end do
*
	do i=1,n
	  gobj(i) = c1(i) + dlog(x(i)/t) 
	end do
*
* Bounds on variables.
*
	j=1
	do i=1,n
	  cb(j)=x(i)-0.000001d0
	  cb(j+1)=1.d38-x(i)
	  j=j+2
	end do
*
*
* Equality Constraints.
*
	e(1)=x(1)+2.d0*x(2)+2.d0*x(3)+x(6)+x(10)-2.d0

	e(2)=x(4)+2.d0*x(5)+x(6)+x(7)-1.d0

	e(3)=x(3)+x(7)+x(8)+2.d0*x(9)+x(10)-1.d0
*
* Jacobian of the equality constraints.
*
	ge(1)=1.d0
	ge(2)=2.d0
	ge(3)=2.d0
	ge(4)=1.d0
	ge(5)=1.d0
	ge(6)=2.d0
	ge(7)=1.d0
	ge(8)=1.d0
	ge(9)=1.d0
	ge(10)=1.d0
	ge(11)=1.d0
	ge(12)=2.d0
	ge(13)=1.d0
	ge(14)=1.d0
*
* INEquality Constraints.
*
* Jacobian of the INEquality constraints.
*
      return
      end
*---------------------------------------------------HS112.for