*---------------------------------------------------------
* Date created:  February 8, 2001
* 
* Robust Stability of linear systems
* Floudas & Visweswaran Quadratic Optimization,
* Princeton University
*
* Dr. Neculai Andrei
* Research Institute for Informatics,
* 8-10, Averescu Avenue, Bucharest 1, Romania
* E-mail: nandrei@u3.ici.ro
* web: 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)
*
	write(1,10)
10	format(5x,'Example of a Nonlinear Programming Problem.')
	write(1,11)
11	format(5x,'Robust Stability of Linear systems')
	write(1,12)
12	format(5x,'February 8, 2001')
*
      n=8
      m=6
      me=5
      mb=2*n
      nszc=12
      nsze=18
*
* Initial Point:
*
        x(1)=8.d0
        x(2)=4.d0
        x(3)=6.d0
	x(4)=2.d0
	x(5)=1.d0
	x(6)=9.d0
	x(7)=1.d0
	x(8)=4.d0
*
* 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)=2
	icge(3)=1
	icge(4)=2
	icge(5)=5
	icge(6)=1
	icge(7)=2
	icge(8)=3
	icge(9)=1
	icge(10)=2
	icge(11)=3
	icge(12)=1
	icge(13)=4
	icge(14)=1
	icge(15)=2
	icge(16)=4
	icge(17)=3
	icge(18)=5
*
* Starting adress for the columns
*	                  
        ipge(1)=1
        ipge(2)=3
        ipge(3)=6
        ipge(4)=9
        ipge(5)=12
        ipge(6)=0
        ipge(7)=14
        ipge(8)=17
        ipge(9)=19
*
* 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)=5
	icgc(12)=6
*
* Starting adress for the columns
*
	ipgc(1)=1
	ipgc(2)=3
	ipgc(3)=5
	ipgc(4)=0
	ipgc(5)=0
	ipgc(6)=7
	ipgc(7)=0
	ipgc(8)=0
	ipgc(9)=13
*
      return
      end
*

*--------------------------------------------------------------
* Date created:  February 8, 2001
*
* Robust stability of linear systems
* Floudas & Visweswaran, Quadratic Optimization,
* Princeton University
*--------------------------------------------------------------
*
      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)
*
* Objective function, and its gradient.
*
	objf= x(6)
*
* Gradient of the Objective Function
*
	do i=1,n
	  gobj(i)=0.d0
	end do
	gobj(6)=1.d0
*	
* Bounds on variables.
*
      j=1
      do i=1,n
	cb(j)=x(i)
	cb(j+1)=10.d0-x(i)
	j=j+2
      end do
*
*
* -- Equality Constraints
*
	e(1)= x(5)*x(7) - (x(4)+10.d0*x(2)+10.d0*x(3))*x(7)
     *        +2.d0*x(1)

	e(2)= (x(2)+x(3)+10.d0)*x(7) - 10.d0*x(4) - x(1)

	e(3)= x(4) - x(3)*x(8)

	e(4)= x(5)-x(7)

	e(5)= x(2)-x(8)
*
* -- InEquality Constraints
*
	c(1) = 800.d0 + 800.d0*x(6) - x(1)

	c(2) = x(1) - 800.d0 + 800.d0*x(6)

	c(3) = 4.d0 + 2.d0*x(6) - x(2)

	c(4)= x(2) - 4.d0 + 2.d0*x(6)

	c(5)= 6.d0 + 3.d0*x(6) - x(3)

	c(6)= x(3) - 6.d0 + 3.d0*x(6)
* 
*
* -- Jacobian of the Equality Constraints
*
* Col 1
        ge(1)=2.d0
        ge(2)=-1.d0
* Col 2
        ge(3)=-10.d0*x(7)
        ge(4)=x(7)
        ge(5)=1.d0
* Col 3
        ge(6)=-10.d0*x(7)
        ge(7)=x(7)
        ge(8)=-x(8)
* Col 4
        ge(9)=-x(7)
        ge(10)=-10.d0
        ge(11)=1.d0
* Col 5
        ge(12)=x(7)
        ge(13)=1.d0
* Col 6
* Col 7
        ge(14)=x(5) -(x(4)+10.d0*x(2)+10.d0*x(3))
        ge(15)=x(2)+x(3)+10.d0
        ge(16)=-1.d0
* Col 8
        ge(17)=-x(3)
        ge(18)=-1.d0
*
* -- Jacobian of the Inequality constraints.
*
* Col 1
        gc(1)=-1.d0
        gc(2)=1.d0
* COl 2
        gc(3)=-1.d0
        gc(4)=1.d0
* Col 3
        gc(5)=-1.d0
        gc(6)=1.d0
* Col 4
* Col 5
* Col 6
        gc(7)=800.d0
        gc(8)=800.d0
        gc(9)=2.d0
        gc(10)=2.d0
        gc(11)=3.d0
        gc(12)=3.d0
*
      return
      end
*-------------------------------------------------FV2.for