\$title Princeton Bilevel Optimization Example 9.1.2 (FLDS912,SEQ=28) \$ontext Test problem 9.2.3 in Handbook of Test Problems in Local and Global Optimization Test problem 9.1.2 on http://titan.princeton.edu/TestProblems/chapter9.html References: Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999. Liu, Y H, and Hart, S M, Characterizing an Optimal Solution to the Linear Bilevel Programming Problem. European Journal of Operational Research 79 (1994), 164-166. Contributor: Alex Meeraus and Jan-H. Jagla, December 2009 \$offtext *Solution of problem 9.1.2 on the web scalar x_l / 4 / y_l / 4 / tol / 1e-6 /; variables z, z_in; positive variables x, y; equation ob, c2, c3, c4, c5; ob.. - x - 3*y =e= z; c2.. - x + y =l= 3; c3.. x + 2*y =l= 12; c4.. 4*x - y =l= 12; c5.. - y =l= 0; model bilevel / all /; \$echo bilevel x min y c2 c3 c4 c5 > "%emp.info%" *Start from reported solution x.l = x_l; y.l = y_l; solve bilevel using EMP minimizing z; abort\$( (abs(x.l - x_l) > tol) or (abs(y.l - y_l) > tol) ) 'Deviated from reported solution';