Largest Small Hexagon nco Ipopt GAMS short P(I) -> P(I++1) -> 0 TOTAREA TOTAL AREA OF THE HEXAGON EQUATIONS AREADEF(I) AREA DEFINITION FOR TRIANGLE I. MAXDIST(I,J) MAXIMAL DISTANCE BETWEEN I AND J OBJ1 FIRST DEFINITION OF OBJECTIVE OBJ2 SECOND DEFINITION OF OBJECTIVE; MAXDIST(I,J)$(ORD(I) LT ORD(J)).. SQR(X(I)-X(J))+SQR(Y(I)-Y(J)) =L= 1; AREADEF(I).. AREA(I) =E= 0.5*(X(I)*Y(I++1)-Y(I)*X(I++1)) ; OBJ1.. TOTAREA =E= 0.5*SUM(I,X(I)*Y(I++1)-Y(I)*X(I++1)); OBJ2.. TOTAREA =E= SUM(I,AREA(I)); MODEL SMALL /MAXDIST,OBJ1/ LARGE /MAXDIST,OBJ2,AREADEF/ ; * * INITIAL CONDITIONS * X.FX("1") = 0; Y.FX("1") = 0; Y.FX("2") = 0; X.L("2") = 0.5; X.L("3") = 0.5; X.L("4") = 0.5; X.L("5") = 0; X.L("6") = 0; Y.L("3") = 0.4; Y.L("4") = 0.8; Y.L("5") = 0.8; Y.L("6") = 0.4; * *syntax for setting GAMS options * option iterlim=500; SOLVE LARGE USING NLP MAXIMIZING TOTAREA; ]]> Finds the largest area possible for a hexagon with a diameter of 1 with 22 equations, 19 variables, and 97 non-zeroes.