*---------------------------------------------------------
* Date created:  December 23, 1997.
*           
* Hock & Schittkowski, 
* Test Examples for Nonlinear Programming Codes.
* Springer-Verlag, 1981.
* Problem 83, page 102
*
* 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 83, pp.102')
*
      n=5
      m=6
      me=0
      mb=2*n
      nszc=26
      nsze=0
*
* Initial Point
*
	x(1)=78.001d0
	x(2)=33.001d0
	x(3)=27.001d0
	x(4)=27.001d0
	x(5)=27.001d0
*
* 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.
*
*
* Starting address of the 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)=1
	icgc(8)=2
	icgc(9)=3
	icgc(10)=4

	icgc(11)=1
	icgc(12)=2
	icgc(13)=3
	icgc(14)=4
	icgc(15)=5
	icgc(16)=6

	icgc(17)=1
	icgc(18)=2
	icgc(19)=5
	icgc(20)=6

	icgc(21)=1
	icgc(22)=2
	icgc(23)=3
	icgc(24)=4
	icgc(25)=5
	icgc(26)=6
*
* Starting address of the columns of the Jacobian of the INEqualities.
*
	ipgc(1)=1
	ipgc(2)=7
	ipgc(3)=11
	ipgc(4)=17
	ipgc(5)=21
	ipgc(6)=27
*
      return
      end
*
*--------------------------------------------------------------
* Date created:  December 23, 1997
* Schittkowski, prob. 83, pp.102
*--------------------------------------------------------------
*
      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 a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12

*
* Objective function, and its gradient.
*
        objf=   5.3578547d0*x(3)*x(3) + 0.8356891d0*x(1)*x(5) +
     1		37.293239d0*x(1) - 40792.141d0
*
	gobj(1)=37.293239d0 + 0.8356891d0*x(5)
	gobj(2)=0.d0
	gobj(3)=2.d0*5.3578547d0*x(3)
	gobj(4)=0.d0
	gobj(5)=0.8356891d0*x(1)
*
* Bounds on variables.
*
	cb(1)=x(1)-78.d0
	cb(2)=102.d0-x(1)
	cb(3)=x(2)-33.d0
	cb(4)=45.d0-x(2)
	cb(5)=x(3)-27.d0
	cb(6)=45.d0-x(3)
	cb(7)=x(4)-27.d0
	cb(8)=45.d0-x(4)
	cb(9)=x(5)-27.d0
	cb(10)=45.d0-x(5)
*
*
* Equality Constraints.
*
*
* Jacobian of the equality constraints.
*
*
* INEquality Constraints.
*
	a1=85.334407d0
	a2=0.0056858d0
	a3=0.0006262d0
	a4=0.0022053d0
	a5=80.51249d0
	a6=0.0071317d0
	a7=0.0029955d0
	a8=0.0021813d0
	a9=9.300961d0
	a10=0.0047026d0
	a11=0.0012547d0
	a12=0.0019085d0

*
	c(1)=a1 + a2*x(2)*x(5) + a3*x(1)*x(4) - a4*x(3)*x(5)
	c(2)=92.d0 - c(1)
	c(3)=a5 +a6*x(2)*x(5) + a7*x(1)*x(2) + a8*x(3)*x(3) -90.d0
	c(4)=20.d0 - c(3)
	c(5)=a9 + a10*x(3)*x(5)+a11*x(1)*x(3)+a12*x(3)*x(4)-20.d0
	c(6)=5.d0 - c(5)
*
* Jacobian of the INEquality constraints.
c1
	gc(1)=a3*x(4)
	gc(2)=-a3*x(4)
	gc(3)=a7*x(2)
	gc(4)=-a7*x(2)
	gc(5)=a11*x(3)
	gc(6)=-a11*x(3)
c2
	gc(7)=a2*x(5)
	gc(8)=-a2*x(5)
	gc(9)=a6*x(5)+a7*x(1)
	gc(10)=-(a6*x(5)+a7*x(1))
c3
	gc(11)=-a4*x(5)
	gc(12)=a4*x(5)
	gc(13)=2.d0*a8*x(3)
	gc(14)=-2.d0*a8*x(3)
	gc(15)=a10*x(5)+a11*x(1)+a12*x(4)
	gc(16)=-(a10*x(5)+a11*x(1)+a12*x(4))
c4
	gc(17)=a3*x(1)
	gc(18)=-a3*x(1)
	gc(19)=a12*x(3)
	gc(20)=-a12*x(3)
c5
	gc(21)=a2*x(2)-a4*x(3)
	gc(22)=-(a2*x(2)-a4*x(3))
	gc(23)=a6*x(2)
	gc(24)=-a6*x(2)
	gc(25)=a10*x(3)
	gc(26)=-a10*x(3)
*
      return
      end
*-----------------------------------------------HS83.for