*-----------------------------------------------------------
* Date created: June 2, 2001
*
* Combustion of Propan.  
* Reduced version.
* A least squares approach. 
* 
* Averick, Carter, More,
* The MINPACK2 Test Problem Collection (Preliminary Version)
* Argonne National Laboratory
* Technical Memorandum No. 150, May 1991. 
* 
*
* The problem is to solve an algebraic system of 5 nonlinear 
* equations with 5 unknowns. 
* In this program a least squares approach is considered, i.e.
* to minimize the summ of squares of all equations.
* Additionally the nonnegativity of variables is introduced.
* In the example PROPR (please see SPENPROB collection) the
* problem is to minimize a constant function subject to
* 5 nonlinear equality constraints.               
* SPENBAR package gives the same solution.
*
* Dr. Neculai Andrei
* Research Institute for Informatics,
* 8-10, Averescu Avenue, Bucharest 1, Romania
* E-mail: nandrei@u3.ici.ro
* web: http://www.ici.ro/camo
*-----------------------------------------------------------
*
	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,'Combustion of Propane. A least squares approach ')
	write(1,11)
11	format(5x,'Simple bounded optimization')           
      write(1,12)
12    format(5x,'Reduced version')      
*
* Dimension of the problem:
*
	n=5
	m=0
	me=0
	mb=5
	nszc=0
	nsze=0
*
* Initial point:
*
	x(1)=10.d0 
	x(2)=10.d0
	x(3)=0.05d0
	x(4)=50.d0
	x(5)=0.05d0
*
* Index vector for simple bounds: cb >= 0.
*                
      do i=1,n
        sb(i)=i
      end do  
*
* Rows indices of the nonzeros of the Jacobian of the Inequalities
*
*
* Starting address of columns of the Jacobian of the Inequalities
*
*
* 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: June 2, 2001
* Combustion of Propan. Reduced version.
* A least squares approach. 
*--------------------------------------------------------------
*
	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) 
*
      double precision fjac(5,5)
      double precision t(5)
      double precision r
      double precision r5,r6,r7,r8,r9,r10
*
*
* Objective function and its gradient:
*
      r5=0.193d0
      r6=0.410621754d-3
      r7=0.5451766686d-3
      r8=0.44975d-6
      r9=0.3407354178d-4
      r10=0.9615d-6
      r=10.d0           
*
* Objective
*
         t(1) = x(1)*x(2)+x(1)-3.d0*x(5)
*         
         t(2) = 2.d0*x(1)*x(2)+x(1)+2.d0*r10*x(2)*x(2)+
     *          x(2)*x(3)*x(3)+r7*x(2)*x(3)+r9*x(2)*x(4)+
     *          r8*x(2)-r*x(5)    
                                                      
         t(3) = 2.d0*x(2)*x(3)*x(3)+r7*x(2)*x(3)+
     *          2.d0*r5*x(3)*x(3)+r6*x(3)-8.d0*x(5)
         
         t(4) = r9*x(2)*x(4)+2.d0*x(4)*x(4)-4.d0*r*x(5)
                                 
         t(5) = x(1)*x(2)+x(1)+r10*x(2)*x(2)+x(2)*x(3)*x(3)+
     *          r7*x(2)*x(3)+r9*x(2)*x(4)+r8*x(2)+r5*x(3)*x(3)+
     *          r6*x(3)+x(4)**2-1.d0                        
*
      objf=0.d0
      do i=1,n
        objf=objf+t(i)*t(i)
      end do  
*
* Gradient of the objective:
*
         do 40 j = 1, n                                                       
            do 30 i = 1, n                                                
               fjac(i,j) = 0.d0                                               
30          continue                                                          
40       continue                                                             
*                                                                              
         fjac(1,1) = x(2)+1.d0                                                      
         fjac(1,2) = x(1)
         fjac(1,5) =-3.d0
*
         fjac(2,1) = 2.d0*x(2)+1.d0
         fjac(2,2) = 2.d0*x(1)+4.d0*r10*x(2)+x(3)**2+
     *               r7*x(3)+r9*x(4)+r8
         fjac(2,3) = 2.d0*x(2)*x(3)+r7*x(2)
         fjac(2,4) = r9*x(2)
         fjac(2,5) = -r
*
         fjac(3,2) = 2.d0*x(3)*x(3)+r7*x(3)
         fjac(3,3) = 4.d0*x(2)*x(3)+r7*x(2)+4.d0*r5*x(3)+r6
         fjac(3,5) = -8.d0
*
         fjac(4,2) = r9*x(4)
         fjac(4,4) = r9*x(2)+4.d0*x(4)
         fjac(4,5) = -4.d0*r
*
         fjac(5,1) = x(2)+1.d0
         fjac(5,2) = x(1)+2.d0*r10*x(2)+x(3)**2+r7*x(3)+
     *               r9*x(4)+r8    
         fjac(5,3) = 2.d0*x(2)*x(3)+r7*x(2)+2.d0*r5*x(3)+r6
         fjac(5,4) = r9*x(2)+2.d0*x(4)
*           
      do i=1,n
        gobj(i)=0.d0
        do j=1,n
          gobj(i)=gobj(i)+fjac(j,i)*2.d0*t(j)
        end do
      end do                      
*
* Bounds on variables:
*                                    
      do i=1,11
        cb(i)=x(i)
      end do  
*
* Constraints. (Inequalities):
*
*
* Jacobian of the inequalities constraints:
*
*
* Constraints. (Equalities):
*
*
* Jacobian of the equality constraints:
*
*
	return
	end
*------------------------------------------------PROPRLS.for