(!******************************************************
   Mosel Example Problems
   ======================

   file inscribedsquare.mos 
   ````````````````````````
   Computes a maximal inscribing square for the curve 
   (sin(t)*cos(t), sin(t)*t), t in [-pi,pi]

   Source: https://www.minlplib.org/inscribedsquare01.html

   x2..x5 are the four values of the parameter t. 
   x6 and x7 are the (x,y) coordinates of the first corner of the square. 
   (x8, x9) is a vector pointing to a second vertex, all the other vertices 
   are given by a combination of these four values. 
   The length of the vector (x8,x9) is exactly the side length of the
   square, which we are maximizing, that is, the square of it, to keep it nicer.
   
   (c) 2023 Fair Isaac Corporation
       author: S. Heipcke, July 2023
*******************************************************!)
model "inscribedsquare"
 uses "mmxnlp"
 parameters
   ALG=1      ! Solver choice:  1: global, 2: SLP, 3: Knitro
 end-parameters

 declarations
   x2,x3,x4,x5,x6,x7,x8,x9: mpvar
 end-declarations

! Variable bounds
 x2 >= -3.14159265358979; x2 <= 3.14159265358979;
 x3 >= -3.14159265358979; x3 <= 3.14159265358979;
 x4 >= -3.14159265358979; x4 <= 3.14159265358979;
 x5 >= -3.14159265358979; x5 <= 3.14159265358979;
 x6 is_free
 x7 is_free

(! Optionally, set initial values:
 setinitval(x2, -3.14159265358979)
 setinitval(x3, -1.5707963267949)
 setinitval(x4, 1.5707963267949)
 setinitval(x5, 1.5707963267949)
 setinitval(x6, 1.22464679914735E-16)
 setinitval(x7, 3.84734138744358E-16)
 setinitval(x8, 1)
 setinitval(x9, 1)
!)

 Obj:= x8^2 + x9^2;

! Constraints
 E2:= sin(x2)*cos(x2) - x6 = 0;
 E3:= sin(x2)*x2 - x7 = 0;
 E4:= sin(x3)*cos(x3) - x6 - x8 = 0;
 E5:= sin(x3)*x3 - x7 - x9 = 0;
 E6:= sin(x4)*cos(x4) - x6 + x9 = 0;
 E7:= sin(x4)*x4 - x7 - x8 = 0;
 E8:= sin(x5)*cos(x5) - x6 - x8 + x9 = 0;
 E9:= sin(x5)*x5 - x7 - x8 - x9 = 0;

 setparam("XNLP_VERBOSE",true)        ! Uncomment to see detailed output
 case ALG of
  1: writeln("Using global solver")
  2: do
     writeln("Using SLP as local solver")
    ! Use multi-start heuristic
     addmultistart("random points", XNLP_MSSET_INITIALVALUES, 100)
     setparam("XPRS_NLPSOLVER", 1)       ! Use a local NLP solver
     setparam("XNLP_SOLVER", 0)          ! Select SLP as local solver
   end-do
  3: do
     writeln("Using Knitro as local solver")
    ! Use multi-start heuristic
     addmultistart("random points", XNLP_MSSET_INITIALVALUES, 100)
     setparam("XPRS_NLPSOLVER", 1)       ! Use a local NLP solver
     setparam("XNLP_SOLVER", 1)          ! Select Knitro as local solver
   end-do
 end-case

 maximize(Obj)

 writeln("Solution value: ", getobjval)
 writeln("Corner point: ", x6.sol, ",", x7.sol)
 writeln("Side vector: ", x8.sol, "  ", x9.sol)
 writeln("t=", x2.sol, "  ", x3.sol, "  ", x4.sol, "  ", x5.sol)
 
end-model