C     =================================================================
C     File: f12.f
C     =================================================================

C     =================================================================
C     Module: Subroutines that define the problem
C     =================================================================

C     Last update of any of the component of this module: 
 
C     July 13, 2006.

C     Users are encouraged to download periodically updated versions of 
C     this code at the TANGO home page:
 
C     www.ime.usp.br/~egbirgin/tango/ 

C     F12 Problem
C     Problem proposed in:
C     C. N. Menezes, P. M. Pardalos, M. G. C. Resende. "GRASP for 
C     Nonlinear Optimization", AT&T Labs Research Technical Report 
C     TD-6DUTRG, 2005.

C     ******************************************************************
C     ******************************************************************

      subroutine inip(n,x,l,u,m,lambda,rho,equatn,linear)

      implicit none

C     This subroutine must set some problem data. For achieving this 
C     objective YOU MUST MODIFY it according to your problem. See below 
C     where your modifications must be inserted.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     This subroutine has no input parameters.
C
C     On Return
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              initial point,
C
C     l        double precision l(n),
C              lower bounds on x,
C
C     u        double precision u(n),
C              upper bounds on x,
C
C     m        integer,
C              number of constraints (excluding the bounds),
C
C     lambda   double precision lambda(m),
C              initial estimation of the Lagrange multipliers,
C
C     rho      double precision rho(m),
C              initial penalty parameters.
C
C     equatn   logical equatn(m)
C              for each constraint j, set equatn(j) = .true. if it is an 
C              equality constraint of the form c_j(x) = 0, and set 
C              equatn(j) = .false. if it is an inequality constraint of 
C              the form c_j(x) <= 0,
C
C     linear   logical linear(m)
C              for each constraint j, set linear(j) = .true. if it is a 
C              linear constraint, and set linear(j) = .false. if it is a
C              nonlinear constraint.

C     SCALAR ARGUMENTS
      integer m,n

C     ARRAY ARGUMENTS
      logical equatn(*),linear(*)
      double precision l(*),lambda(*),rho(*),u(*),x(*)

C     LOCAL SCALARS
      integer i

C     ******************************************************************
C     FROM HERE ON YOU MUST MODIFY THE SUBROUTINE TO SET YOUR PROBLEM
C     DATA:
C     ******************************************************************

C     Number of variables

      n = 2

C     Initial point

      do i = 1,n
          x(i) = 0.0d0
      end do

C     Lower and upper bounds

      do i = 1,n
          l(i) = -5.0d0
          u(i) =  5.0d0
      end do

C     Number of constraints (equalities plus inequalities)

      m = 0

C     ******************************************************************
C     STOP HERE YOUR MODIFICATIONS OF SUBROUTINE INIP.
C     ******************************************************************

      end

C     ******************************************************************
C     ******************************************************************

      subroutine evalf(n,x,f,flag)

      implicit none

C     This subroutine must compute the objective function. For achieving 
C     this objective YOU MUST MODIFY it according to your problem. See 
C     below where your modifications must be inserted.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     On Return
C
C     f        double precision,
C              objective function value at x,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the objective 
C              function. (For example, trying to compute the square root 
C              of a negative number, dividing by zero or a very small 
C              number, etc.) If everything was o.k. you must set it 
C              equal to zero.

C     SCALAR ARGUMENTS
      integer flag,n
      double precision f

C     ARRAY ARGUMENTS
      double precision x(n)

C     LOCAL SCALARS

C     LOCAL ARRAYS

C     Objective function

C     ******************************************************************
C     FROM HERE ON YOU MUST MODIFY THE SUBROUTINE TO SET YOUR OBJECTIVE
C     FUNCTION:
C     ******************************************************************

      flag = 0

C     F12

      f = 0.5d0 * x(1) ** 2.0d0
     +  + 0.5d0 * ( 1.0d0 - cos( 2.0d0 * x(1) ) )
     +  +          x(2) ** 2.0d0

C     ******************************************************************
C     STOP HERE YOUR MODIFICATIONS OF SUBROUTINE EVALF.
C     ******************************************************************

      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalg(n,x,g,flag)

      implicit none

C     This subroutine must compute the gradient vector of the objective 
C     function. For achieving these objective YOU MUST MODIFY it in the 
C     way specified below. However, if you decide to use numerical 
C     derivatives (we dont encourage this option at all!) you dont need
C     to modify evalg.
C
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     On Return
C
C     g        double precision g(n),
C              gradient vector of the objective function evaluated at x,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of any component 
C              of the gradient vector. (For example, trying to compute 
C              the square root of a negative number, dividing by zero or 
C              a very small number, etc.) If everything was o.k. you 
C              must set it equal to zero.

C     SCALAR ARGUMENTS
      integer flag,n

C     ARRAY ARGUMENTS
      double precision g(n),x(n)

C     LOCAL SCALARS

C     LOCAL ARRAYS

C     Gradient vector

C     ******************************************************************
C     FROM HERE ON YOU MUST MODIFY THE SUBROUTINE TO SET THE GRADIENT
C     VECTOR OF YOUR OBJECTIVE FUNCTION: 
C     ******************************************************************

      flag = 0

C     F12

      g(1) = x(1)
     +  + sin( 2.0d0 * x(1) ) 

      g(2) = x(2) * 2.0d0

C     ******************************************************************
C     STOP HERE YOUR MODIFICATIONS OF SUBROUTINE EVALG. 
C     ******************************************************************
 
      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalh(n,x,hlin,hcol,hval,nnzh,flag)

      implicit none

C     This subroutine might compute the Hessian matrix of the objective 
C     function. For achieving this objective YOU MAY MODIFY it according 
C     to your problem. To modify this subroutine IS NOT MANDATORY. See 
C     below where your modifications must be inserted.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     On Return
C
C     nnzh     integer,
C              number of perhaps-non-null elements of the computed 
C              Hessian,
C
C     hlin     integer hlin(nnzh),
C              see below,
C
C     hcol     integer hcol(nnzh),
C              see below,
C
C     hval     double precision hval(nnzh),
C              the non-null value of the (hlin(k),hcol(k)) position 
C              of the Hessian matrix of the objective function must 
C              be saved at hval(k). Just the lower triangular part of
C              Hessian matrix must be computed,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the Hessian
C              matrix of the objective funtion. (For example, trying 
C              to compute the square root of a negative number, 
C              dividing by zero or a very small number, etc.) If 
C              everything was o.k. you must set it equal to zero.

C     SCALAR ARGUMENTS
      integer flag,n,nnzh

C     ARRAY ARGUMENTS
      integer hcol(*),hlin(*)
      double precision hval(*),x(n)

C     ******************************************************************
C     FROM HERE ON YOU MAY (OPTIONALY) MODIFY THE SUBROUTINE TO SET THE 
C     HESSIAN MATRIX OF YOUR OBJECTIVE FUNCTION: 
C     ******************************************************************

      flag = -1

C     ******************************************************************
C     STOP HERE YOUR MODIFICATIONS OF SUBROUTINE EVALH. 
C     ******************************************************************
 
      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalc(n,x,ind,c,flag)

      implicit none

C     This subroutine must compute the i-th constraint of your problem. 
C     For achieving this objective YOU MUST MOFIFY it according to your 
C     problem. See below the places where your modifications must be 
C     inserted.
C
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     ind      integer,
C              index of the constraint to be computed,
C
C     On Return
C
C     c        double precision,
C              ind-th constraint evaluated at x,
C
C     flag     integer
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the 
C              constraint. (For example, trying to compute the square 
C              root of a negative number, dividing by zero or a very 
C              small number, etc.) If everything was o.k. you must set 
C              it equal to zero.
 
C     SCALAR ARGUMENTS
      integer ind,flag,n
      double precision c

C     ARRAY ARGUMENTS
      double precision x(n)

C     Constraints

C     ******************************************************************
C     FROM HERE ON YOU MUST MODIFY THE SUBROUTINE TO SET YOUR
C     CONSTRAINTS: 
C     ******************************************************************

      flag = -1

C     ******************************************************************
C     STOP HERE YOUR MODIFICATIONS OF SUBROUTINE EVALC. 
C     ******************************************************************
 
      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evaljac(n,x,ind,indjac,valjac,nnzjac,flag)

      implicit none

C     This subroutine must compute the gradient of the constraint i. For 
C     achieving these objective YOU MUST MODIFY it in the way specified 
C     below.
C
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     ind      integer,
C              index of the constraint whose gradient will be computed,
C
C     On Return
C
C     nnzjac   integer,
C              number of perhaps-non-null elements of the computed 
C              gradient,
C
C     indjac   integer indjac(nnzjac),
C              see below,
C
C     valjac   double precision valjac(nnzjac),
C              the non-null value of the partial derivative of the i-th
C              constraint with respect to the indjac(k)-th variable must 
C              be saved at valjac(k).
C
C     flag     integer
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the 
C              constraint. (For example, trying to compute the square 
C              root of a negative number, dividing by zero or a very 
C              small number, etc.) If everything was o.k. you must set 
C              it equal to zero.

C     SCALAR ARGUMENTS
      integer flag,ind,n,nnzjac

C     ARRAY ARGUMENTS
      integer indjac(n)
      double precision x(n),valjac(n)

C     Sparse gradient vector of the ind-th constraint

C     ******************************************************************
C     FROM HERE ON YOU MUST MODIFY THE SUBROUTINE TO SET THE GRADIENTS  
C     OF YOUR CONSTRAINTS: 
C     ******************************************************************

      flag = -1

C     ******************************************************************
C     STOP HERE YOUR MODIFICATIONS OF SUBROUTINE EVALJAC. 
C     ******************************************************************
 
      end

C     ******************************************************************
C     ******************************************************************
 
      subroutine evalhc(n,x,ind,hclin,hccol,hcval,nnzhc,flag)

      implicit none

C     This subroutine might compute the Hessian matrix of the ind-th
C     constraint. For achieving this objective YOU MAY MODIFY it 
C     according to your problem. To modify this subroutine IS NOT 
C     MANDATORY. See below where your modifications must be inserted.
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     ind      integer,
C              index of the constraint whose Hessian will be computed,
C
C     On Return
C
C     nnzhc    integer,
C              number of perhaps-non-null elements of the computed 
C              Hessian,
C
C     hclin    integer hclin(nnzhc),
C              see below,
C
C     hccol    integer hccol(nnzhc),
C              see below,
C
C     hcval    double precision hcval(nnzhc),
C              the non-null value of the (hclin(k),hccol(k)) position 
C              of the Hessian matrix of the ind-th constraint must 
C              be saved at hcval(k). Just the lower triangular part of
C              Hessian matrix must be computed,
C
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the Hessian
C              matrix of the ind-th constraint. (For example, trying 
C              to compute the square root of a negative number, 
C              dividing by zero or a very small number, etc.) If 
C              everything was o.k. you must set it equal to zero.

C     SCALAR ARGUMENTS
      integer flag,ind,n,nnzhc

C     ARRAY ARGUMENTS
      integer hccol(*),hclin(*)
      double precision hcval(*),x(n)

C     ******************************************************************
C     FROM HERE ON YOU MAY (OPTIONALY) MODIFY THE SUBROUTINE TO SET THE 
C     HESSIANS OF YOUR CONSTRAINTS: 
C     ******************************************************************

      flag = -1

C     ******************************************************************
C     STOP HERE YOUR MODIFICATIONS OF SUBROUTINE EVALHC. 
C     ******************************************************************
 
      end

C     ******************************************************************
C     ******************************************************************

      subroutine evalhlp(n,x,m,lambda,p,hp,goth,flag)

      implicit none

C     This subroutine might compute the product of the Hessian of the
C     Lagrangian times vector p (just the Hessian of the objective 
C     function in the unconstrained or bound-constrained case). 
C     
C     Parameters of the subroutine:
C
C     On Entry:
C
C     n        integer,
C              number of variables,
C
C     x        double precision x(n),
C              current point,
C
C     m        integer,
C              number of constraints,
C
C     lambda   double precision lambda(m),
C              vector of Lagrange multipliers,
C
C     p        double precision p(n),
C              vector of the matrix-vector product,
C
C     goth     logical,
C              can be used to indicate if the Hessian matrices were
C              computed at the current point. It is set to .false.
C              by the optimization method every time the current
C              point is modified. Sugestion: if its value is .false. 
C              then compute the Hessians, save them in a common 
C              structure and set goth to .true.. Otherwise, just use 
C              the Hessians saved in the common block structure,
C
C     On Return
C
C     hp       double precision hp(n),
C              Hessian-vector product,
C
C     goth     logical,
C              see above,
C              
C     flag     integer,
C              You must set it to any number different of 0 (zero) if 
C              some error ocurred during the evaluation of the 
C              Hessian-vector product. (For example, trying to compute 
C              the square root of a negative number, dividing by zero 
C              or a very small number, etc.) If everything was o.k. you 
C              must set it equal to zero.

C     SCALAR ARGUMENTS
      logical goth
      integer flag,m,n

C     ARRAY ARGUMENTS
      double precision hp(n),lambda(m),p(n),x(n)

      flag = - 1

      end

C     ******************************************************************
C     ******************************************************************

      subroutine endp(n,x,l,u,m,lambda,rho,equatn,linear)

      implicit none

C     This subroutine can be used to do some extra job after the solver
C     has found the solution,like some extra statistics, or to save the
C     solution in some special format or to draw some graphical
C     representation of the solution. If the information given by the
C     solver is enough for you then leave the body of this subroutine
C     empty.
C     
C     Parameters of the subroutine:
C
C     The paraemters of this subroutine are the same parameters of
C     subroutine inip. But in this subroutine there are not output
C     parameter. All the parameters are input parameters.

C     SCALAR ARGUMENTS
      integer m,n

C     ARRAY ARGUMENTS
      logical equatn(m),linear(m)
      double precision l(n),lambda(m),rho(m),u(n),x(n)

C     ******************************************************************
C     FROM HERE ON YOU MUST MODIFY THE SUBROUTINE TO COMPLEMENT THE
C     INFORMATION RELATED TO THE SOLUTION GIVEN BY THE SOLVER
C     ******************************************************************

C     ******************************************************************
C     STOP HERE YOUR MODIFICATIONS OF SUBROUTINE ENDP
C     ******************************************************************

      end