* Date created: October 10, 1996.
* Generated during my stay in:
* Bayreuth University, Mathematics Department,
* Prof. Klaus Schittkowski
*            
* Hock & Schittkowski, 
* Test Examples for Nonlinear Programming Codes.
* Springer-Verlag, 1981.
* Problem 81, Page 101. 
*
* 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 pp.101')
	write(1,14)
14	format(5x,'Problem 81')
*
* Dimension of the problem:
*
	n=5		! No. of variables.
	m=0		! No. of inequality constraints.
	me=3		! No. of equality constraints.
	mb=10		! No. of simple bounds on variables.
	nszc=0		! 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) = -2.d0
	x(2) =  2.d0
	x(3) =  2.d0
	x(4) = -1.d0
	x(5) = -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 equalities
*
	icge(1)=1
	icge(2)=3
	icge(3)=1
	icge(4)=2
	icge(5)=3
	icge(6)=1
	icge(7)=2
	icge(8)=1
	icge(9)=2
	icge(10)=1
	icge(11)=2
*
* Starting address of columns of the Jacobian of the equalities
*
	ipge(1)=1
	ipge(2)=3
	ipge(3)=6
	ipge(4)=8
	ipge(5)=10
	ipge(6)=12
*
* Rows indices of the nonzeros of the Jacobian of the INEqualities
*
*
* Starting address of columns of the Jacobian of the INEqualities
*
*
*
	return
	end
*

*--------------------------------------------------------------
* Date created: October 10, 1996
*
* Problem 81. 
* Hock - Schittkowski, pp.101.
*--------------------------------------------------------------
*
	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 = dexp(x(1)*x(2)*x(3)*x(4)*x(5)) -
     1  	0.5d0*(x(1)**3 + x(2)**3 + 1.d0)**2

	gobj(1)= x(2)*x(3)*x(4)*x(5)*objf - 
     1  	  3.d0*(x(1)**3+x(2)**3+1.d0)*x(1)*x(1)

	gobj(2)= x(1)*x(3)*x(4)*x(5)*objf - 
     1	          3.d0*(x(1)**3+x(2)**3+1.d0)*x(2)*x(2)

	gobj(3)= x(1)*x(2)*x(4)*x(5)*objf

	gobj(4)= x(1)*x(2)*x(3)*x(5)*objf

	gobj(5)= x(1)*x(2)*x(3)*x(4)*objf
*
* Bounds on variables:
*
	cb(1)=x(1)+2.3d0
	cb(2)=2.3d0-x(1)
	cb(3)=x(2)+2.3d0
	cb(4)=2.3d0-x(2)
	j=5
	do i=1,n
	   cb(j)=x(i)+ 3.2d0
	   cb(j+1)=3.2d0-x(i)
	   j=j+2
	end do
*
* Constraints. (Inequalities):
*
*
* Jacobian of the inequalities constraints:
*
*
* Constraints. (Equalities):
*
	e(1) = x(1)**2+x(2)**2+x(3)**2+x(4)**2+x(5)**2 - 10.d0
	e(2) = x(2)*x(3) - 5.d0*x(4)*x(5)
	e(3) = x(1)**3 + x(2)**3 +1.d0
* 
* Jacobian of the equalities constraints:
*
	ge(1)=2.d0*x(1)
	ge(2)=3.d0*x(1)*x(1)
	ge(3)=2.d0*x(2)
	ge(4)=x(3)
	ge(5)=3.d0*x(2)*x(2)
	ge(6)=2.d0*x(3)
	ge(7)=x(2)
	ge(8)=2.d0*x(4)
	ge(9)=-5.d0*x(5)
	ge(10)=2.d0*x(5)
	ge(11)=-5.d0*x(4)
*
	return
	end
*---------------------------------------------HS81.for