(!********************************************************************* Mosel NL examples ================= file minsurf.mos ```````````````` Convex NLP problem minimizing the surface between given boundaries. Set parameter OBSTACLE to 'true' to add an additional fixed area in the center of the surface. Based on AMPL model minsurf.mod Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/minsurf/ *** This model cannot be run with a Community Licence for the provided data instance *** (c) 2008 Fair Issac Corporation author: S. Heipcke, Sep. 2008, rev. Mar. 2013 *********************************************************************!) model "minsurf" uses "mmxnlp" parameters OBSTACLE=true N0 = 35 ! Number of points within borders end-parameters declarations N = N0+1 ! Border point index X = 0..N ! Range for x-values Y = 0..N ! Range for y-values HX = 2/N HY = 2/N GAMMA0,GAMMA2: array(X) of real ! Border points parallel to x axis GAMMA1,GAMMA3: array(Y) of real ! Broder points parallel to y axis end-declarations forall(x in X) GAMMA0(x):= 1,5*x*(N-x)/(N/2)^2 forall(y in Y) GAMMA1(y):= 2*y*(N-y)/(N/2)^2 forall(x in X) GAMMA2(x):= 4*x*(N-x)/(N/2)^2 forall(y in Y) GAMMA3(y):= 2*y*(N-y)/(N/2)^2 (! Alternative border definition: forall(x in X) GAMMA0(x):= 2*(if (x <= N/2, x, N-x)/(N/2)) forall(y in Y) GAMMA1(y):= 0*(if (y <= N/2, y, N-y)/(N/2)) forall(x in X) GAMMA2(x):= 2*(if (x <= N/2, x, N-x)/(N/2)) forall(y in Y) GAMMA3(y):= 0*(if (y <= N/2, y, N-y)/(N/2)) !) declarations z: array(X,Y) of mpvar ! Surface height at grid points end-declarations forall(x in X,y in Y) z(x,y) is_free ! Objective function Area:= (HX*HY/2)*sum(x in X | x<N, y in Y | y<N) ( sqrt(1 + ((z(x+1,y)-z(x,y))/HX)^2 + ((z(x,y+1)-z(x,y))/HX)^2) + sqrt(1 + ((z(x+1,y+1)-z(x,y+1))/HX)^2 + ((z(x+1,y+1)-z(x+1,y))/HX)^2) ) ! Fix the boundaries forall(x in X) z(x,0) = GAMMA0(x) forall(y in Y) z(N,y) = GAMMA1(y) forall(x in X) z(x,N) = GAMMA2(x) forall(y in Y) z(0,y) = GAMMA3(y) ! Add an obstacle in the center of the area if OBSTACLE then forall(x,y in ceil(N*0,4)..ceil(N*0,6)) z(x,y) = GAMMA2(ceil(N/2)) end-if setparam("XNLP_verbose", true) minimise(Area) writeln("Solution: ", Area.sol) forall(x in X, y in Y) writeln(x, " ", y, " ", z(x,y).sol) end-model