(!*********************************************************************
   Mosel NL examples
   =================
   file polygon2.mos
   `````````````````
   Maximize the area of polygon of N vertices and diameter of 1. 
   
   The position of vertices is indicated as (rho,theta) coordinates
   where rho denotes the distance to the base point (vertex with number N) 
   and theta the angle from the x-axis.
   
   -- Formulation using a simple Mosel user function --
 
   (c) 2008 Fair Issac Corporation
       Creation: 2002, rev. Feb. 2013
*********************************************************************!)
 
model "Polygon 2"
 uses "mmxnlp"

 parameters
  N=5                               ! Number of vertices
  SOLVER=0                          ! 0: SLP, 1: Knitro
 end-parameters
 
 declarations
  RN = 1..N
  Area: nlctr
  rho : array(RN) of mpvar          ! Distance of vertex from the base point 
  theta : array(RN) of mpvar        ! Angle from x-axis
  D: array(RN,RN) of nlctr          ! Limit on side length
  FunctionArg: array(RN,{"rho","theta"}) of nlctr   ! User function arguments
  AreaFunction : userfunc           ! User function definition
 end-declarations

! Objective: sum of areas. Definition of a user function
 AreaFunction := userfuncMosel("MoselArea")

! Create function arguments
 forall (i in 1..N) do
  FunctionArg(i, "rho")   := rho(i)
  FunctionArg(i, "theta") := theta(i)
 end-do

! Use the Mosel user function in a formula for the objective
 Area := F(AreaFunction,FunctionArg)

! Bounds and start values for decision variables
 forall (i in 1..N-1) do
  rho(i) >= 0.1
  rho(i) <= 1
  setinitval(rho(i),4*i*(N + 1 - i)/((N+1)^2))
  setinitval(theta(i),M_PI*i/N)
 end-do
 
! Third side of all triangles <= 1
 forall(i in 1..N-2, j in i+1..N-1)
  D(i,j) := rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1
 
! Vertices in increasing order 
 forall (i in 2..N-1) theta(i) >= theta(i-1) +.01
 
! Boundary conditions (last vertex above x-axis)
 theta(N-1) <= M_PI

! Uncomment to display user function info
! userfuncinfo(AreaFunction)

! Optional parameter settings
 setparam("xnlp_verbose", true)         ! Enable XNLP output log
 setparam("xnlp_solver", SOLVER)        ! Select the solver

! Solve the problem
 maximise(Area)

! Solution output
 writeln("Area = ", getobjval)
 forall (i in 1..N-1) 
  writeln("V",i,": r=",getsol(rho(i))," theta=",getsol(theta(i)))

! **** Definition of the Mosel user function ****
 public function MoselArea(I: array(Indices: range, Types: set of string) of real): real
  returned := (sum (i in 2..N-1) (I(i,"rho")*I(i-1,"rho")*sin(I(i,"theta")-I(i-1,"theta")))) * 0.5
 end-function

end-model