\$title Largest small Polygon COPS 2.0 #1 (POLYGON,SEQ=229) \$onText Finds the polygon of maximal area, among polygons with nv sides and diameter d <= 1. This model is from the COPS benchmarking suite. See http://www-unix.mcs.anl.gov/~more/cops/. The number of sides can be specified using the command line parameter --nv. COPS performance tests have been reported for nv = 25, 50, 75, 100 Dolan, E D, and More, J J, Benchmarking Optimization Software with COPS. Tech. rep., Mathematics and Computer Science Division, 2000. Graham, R L, The Largest Small Hexagon. J. Combin. Th. 18 (1975), 165-170. Gay, D, AMPL Models. Keywords: nonlinear programming, mathematics \$offText \$if not set nv \$set nv 25 Set i 'sides' / i1*i%nv% /; Alias (i,j); Positive Variable r(i) 'polar radius (distance to fixed vertex)' theta(i) 'polar angle (measured from fixed direction)'; Variable polygon_area; Equation obj distance(i,j) ordered(i); obj.. polygon_area =e= 0.5*sum(j(i + 1), r(i + 1)*r(i)*sin(theta(i + 1) - theta(i))); ordered(i+1).. theta(i) =l= theta(i + 1); distance(i,j)\$(ord(j) > ord(i)).. sqr(r(i)) + sqr(r(j)) - 2*r(i)*r(j)*cos(theta(j) - theta(i)) =l= 1; r.up(i) = 1; theta.up(i) = pi; r.fx('i%nv%') = 0; theta.fx('i%nv%') = pi; r.l(i) = 4*ord(i)*(card(i) + 1 - ord(i))/sqr(card(i) + 1); theta.l(i) = pi*ord(i)/card(i); Model polygon / all /; \$if set workSpace polygon.workSpace = %workSpace% solve polygon using nlp maximizing polygon_area;