*-----------------------------------------------------------
* Date created: February 6, 2001
*
* Ron S. Dembo, 
* A set of geometric programming test problems and
* their solutions.
* Mathematical Programming, vol.10, 1976, pp.208-211.
*
* A 5-stage membrane separation process.
*                                       
* 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,'A 5-stage membrane separation process')
	write(1,11)
11	format(5x,' February 6, 2001')
	write(1,12)
12	format(5x,'Dembo, 1976 - pp.208-211',/)
*
* Dimension of the problem:
*
	n=16
	m=21
	me=0
	mb=32
	nszc=78
	nsze=0
*
* Initial point:
*
	x(1)=0.8d0
	x(2)=0.83d0
	x(3)=0.85d0
	x(4)=0.87d0
	x(5)=0.91d0
	x(6)=0.09d0
	x(7)=0.12d0
	x(8)=0.19d0
	x(9)=0.25d0
	x(10)=0.29d0
	x(11)=512.0d0
	x(12)=13.1d0
	x(13)=71.8d0
	x(14)=640.0d0
	x(15)=650.0d0
	x(16)=5.7d0
*
* 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 Inequalities
*
	icgc(1)=1
	icgc(2)=6
	icgc(3)=7
	icgc(4)=17
	icgc(5)=20
	icgc(6)=21
*
	icgc(7)=2
	icgc(8)=7
	icgc(9)=8
	icgc(10)=16
	icgc(11)=17
	icgc(12)=20
	icgc(13)=21
*
	icgc(14)=3
	icgc(15)=8
	icgc(16)=9
	icgc(17)= 15   
	icgc(18)=16
	icgc(19)=20
	icgc(20)=21
*
	icgc(21)=4
	icgc(22)=9
	icgc(23)=10
	icgc(24)=11
	icgc(25)=14
	icgc(26)=15
	icgc(27)=20
	icgc(28)=21
*
	icgc(29)=5
	icgc(30)=10
	icgc(31)=11
	icgc(32)=14
	icgc(33)=20
	icgc(34)=21
*
	icgc(35)=1
	icgc(36)=6
*
	icgc(37)=2
	icgc(38)=6
	icgc(39)=7
*
	icgc(40)=3
	icgc(41)=7
	icgc(42)=8
	icgc(43)=9
	icgc(44)=19
*
	icgc(45)=4
	icgc(46)=8
	icgc(47)=9
	icgc(48)=18
	icgc(49)=19
*
	icgc(50)=5
	icgc(51)=9
	icgc(52)=10
	icgc(53)=18
*
	icgc(54)=6
	icgc(55)=12
	icgc(56)=13

	icgc(57)=6
	icgc(58)=7
	icgc(59)=12
	icgc(60)=13
	icgc(61)=20
	icgc(62)=21
*
	icgc(63)=7
	icgc(64)=8
	icgc(65)=20
	icgc(66)=21
*
	icgc(67)=8
	icgc(68)=9
	icgc(69)=20
	icgc(70)=21
*
	icgc(71)=9
	icgc(72)=10
	icgc(73)=20
	icgc(74)=21
*
	icgc(75)=10
	icgc(76)=11
	icgc(77)=20
	icgc(78)=21
*
* Starting address of columns of the Jacobian of the Inequalities
*
	ipgc(1)=1
	ipgc(2)=7
	ipgc(3)=14
	ipgc(4)=21
	ipgc(5)=29
	ipgc(6)=35
	ipgc(7)=37
	ipgc(8)=40
	ipgc(9)=45
	ipgc(10)=50
	ipgc(11)=54
	ipgc(12)=57
	ipgc(13)=63
	ipgc(14)=67
	ipgc(15)=71
	ipgc(16)=75
	ipgc(17)=79
*
	return
	end
*

*--------------------------------------------------------------
* 5- stage membrane separation problem
* Dembo, 1976, pp.208-211.
* February 7, 2001
*--------------------------------------------------------------
*
	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)
	real*8 a,b, w,d,v,f,g
*
* Objective function and its gradient:
*
*
	a=1.262626d0
	b=1.231060d0
	w=0.03475d0
	d=0.975d0
	v=0.00975d0
	f=0.002d0
	g=500.0d0
*
	objf = a*(x(12)+x(13)+x(14)+x(15)+x(16)) 
     *        -b*(x(1)*x(12) + x(2)*x(13) +
     *            x(3)*x(14) + x(4)*x(15) +
     *            x(5)*x(16) )
*
	gobj(1)=-b*x(12)
	gobj(2)=-b*x(13)
	gobj(3)=-b*x(14)
	gobj(4)=-b*x(15)
	gobj(5)=-b*x(16)
	gobj(6)=0.d0
	gobj(7)=0.d0
	gobj(8)=0.d0
	gobj(9)=0.d0
	gobj(10)=0.d0
	gobj(11)=0.d0
	gobj(12)=a-b*x(1)
	gobj(13)=a-b*x(2)
	gobj(14)=a-b*x(3)
	gobj(15)=a-b*x(4)
	gobj(16)=a-b*x(5)
*
* Bounds on variables:
*
	cb(1)=x(1)-0.1d0
	cb(2)=0.9d0-x(1)
	cb(3)=x(2)-0.1d0
	cb(4)=0.9d0-x(2)
	cb(5)=x(3)-0.1d0
	cb(6)=0.9d0-x(3)
	cb(7)=x(4)-0.1d0
	cb(8)=0.9d0-x(4)
	cb(9)=x(5)-0.9d0
	cb(10)=1.d0-x(5)
	cb(11)=x(6)-0.0001d0
	cb(12)=0.1d0-x(6)
	cb(13)=x(7)-0.1d0
	cb(14)=0.9d0-x(7)
	cb(15)=x(8)-0.1d0
	cb(16)=0.9d0-x(8)
	cb(17)=x(9)-0.1d0
	cb(18)=0.9d0-x(9)
	cb(19)=x(10)-0.1d0
	cb(20)=0.9d0-x(10)
	cb(21)=x(11)-1.d0
	cb(22)=1000.d0-x(11)
	cb(23)=x(12)-0.000001d0
	cb(24)=500.d0-x(12)
	cb(25)=x(13)-1.d0
	cb(26)=500.d0-x(13)
	cb(27)=x(14)-500.d0
	cb(28)=1000.d0-x(14)
	cb(29)=x(15)-500.d0
	cb(30)=1000.d0-x(15)
	cb(31)=x(16)-0.000001d0
	cb(32)=500.d0-x(16)
*
* Constraints. (INEqualities):
*
	c(1)=x(6)  - w*x(1) - d*x(1)*x(6)  + v*x(1)*x(1)
	c(2)=x(7)  - w*x(2) - d*x(2)*x(7)  + v*x(2)*x(2)
	c(3)=x(8)  - w*x(3) - d*x(3)*x(8)  + v*x(3)*x(3)
	c(4)=x(9)  - w*x(4) - d*x(4)*x(9)  + v*x(4)*x(4)
	c(5)=x(10) - w*x(5) - d*x(5)*x(10) + v*x(5)*x(5)
*
	c(6)=x(7)*x(11) - x(6)*x(11) - x(1)*x(12) +x(6)*x(12)
*
	c(7)=x(8) - x(7)  - f*x(7)*x(12) - f*x(2)*x(13) +
     *       f*x(8)*x(13) + f*x(1)*x(12)
*
	c(8)=1.d0 - x(8) - f*x(8)*x(13) - f*x(3)*x(14) - x(9) +
     *       f*x(2)*x(13) + f*x(9)*x(14)
*
	c(9)=x(3)*x(14) - x(9)*x(14) -x(4)*x(15) - g*x(10) +
     *       g*x(9) + x(8)*x(15)
*
	c(10)=x(4)*x(15) - x(5)*x(16) -x(10)*x(15) - g*x(4) +
     *        x(4)*x(16) + g*x(10)
*
	c(11)=x(4) - f*x(4)*x(16) + f*x(5)*x(16) - 0.9d0
*
	c(12)=1.d0 - f*x(11) + f*x(12) 
*
	c(13)=x(11)-x(12)
	c(14)=x(5)-x(4)
	c(15)=x(4)-x(3)
	c(16)=x(3)-x(2)
	c(17)=x(2)-x(1)
	c(18)=x(10)-x(9)
	c(19)=x(9)-x(8)
*
	c(20)=a*(x(12)+x(13)+x(14)+x(15)+x(16))-
     *        b*(x(1)*x(12) + x(2)*x(13)+
     *           x(3)*x(14) + x(4)*x(15)+
     *           x(5)*x(16)) - 50.d0
*
	c(21)=-a*(x(12)+x(13)+x(14)+x(15)+x(16))+
     *         b*(x(1)*x(12) + x(2)*x(13)+
     *            x(3)*x(14) + x(4)*x(15)+
     *            x(5)*x(16)) + 250.d0
*
*
* Jacobian of the inequalities constraints:
*
* Col 1
	gc(1)=-w - d*x(6) + 2.d0*v*x(1)
	gc(2)=-x(12)
	gc(3)=f*x(12)
	gc(4)=-1.d0
	gc(5)=-b*x(12)
	gc(6)=b*x(12)
* Col 2
	gc(7)=-w - d*x(7) + 2.d0*v*x(2)
	gc(8)=-f*x(13)
	gc(9)=f*x(13)
	gc(10)=-1.d0
	gc(11)=1.d0
	gc(12)=-b*x(13)
	gc(13)=b*x(13)
* Col 3
	gc(14)=-w - d*x(8) + 2.d0*v*x(3)
	gc(15)=-f*x(14)
	gc(16)=x(14)
	gc(17)=-1.d0
	gc(18)=1.d0
	gc(19)=-b*x(14)
	gc(20)=b*x(14)
* Col 4
	gc(21)=-w - d*x(9) + 2.d0*v*x(4)
	gc(22)=-x(15)
	gc(23)=x(15) - g + x(16)
	gc(24)=1.d0 - f*x(16)
	gc(25)=-1.d0
	gc(26)=1.d0
	gc(27)=-b*x(15)
	gc(28)=b*x(15)
* Col 5
	gc(29)=-w - d*x(10) + 2.d0*v*x(5)
	gc(30)=-x(16)
	gc(31)=f*x(16)
	gc(32)=1.d0
	gc(33)=-b*x(16)
	gc(34)=b*x(16)
* Col 6
	gc(35)=1.d0 - d*x(1)
	gc(36)=-x(11) + x(12)
* Col 7
	gc(37)=1.d0 - d*x(2)
	gc(38)=x(11)
	gc(39)=-1.d0 - f*x(12)
* Col 8
	gc(40)=1.d0 - d*x(3)
	gc(41)=1.d0 + f*x(13)
	gc(42)=-1.d0 - f*x(13)
	gc(43)=x(15)
	gc(44)=-1.d0
* Col 9
	gc(45)=1.d0 - d*x(4)
	gc(46)=-1.d0 + f*x(14)
	gc(47)=-x(14) + g
	gc(48)=-1.d0
	gc(49)=1.d0
* Col 10
	gc(50)=1.d0 - d*x(5)
	gc(51)=-g
	gc(52)=-x(15) + g
	gc(53)=1.d0
* Col 11
	gc(54)=x(7) - x(6) 
	gc(55)=-f
	gc(56)=1.d0
* Col 12
	gc(57)=-x(1) + x(6)
	gc(58)=-f*x(7) + f*x(1)
	gc(59)=f
	gc(60)=-1.d0
	gc(61)=a-b*x(1)
	gc(62)=-a+b*x(1)
* Col 13
	gc(63)=-f*x(2) + f*x(8)
	gc(64)=-f*x(8) + f*x(2)
	gc(65)=a-b*x(2)
	gc(66)=-a+b*x(2)
* Col 14
	gc(67)=-f*x(3) + f*x(9)
	gc(68)=x(3) - x(9)
	gc(69)=a-b*x(3)
	gc(70)=-a+b*x(3)
* Col 15
	gc(71)=-x(4) + x(8)
	gc(72)=x(4) - x(10)
	gc(73)=a-b*x(4)
	gc(74)=-a+b*x(4)
* Col 16
	gc(75)=-x(5) + x(4)
	gc(76)=-f*x(4) + f*x(5)
	gc(77)=a-b*x(5)
	gc(78)=-a+b*x(5)
* 
*
	return
	end
*---------------------------------------------------MSP5.for