\$title Princeton Bilevel Optimization Example 9.1.5 (FLDS915,SEQ=31) \$ontext Test problem 9.2.6 in Handbook of Test Problems in Local and Global Optimization Test problem 9.1.5 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. Bard J F, Some properties of the bilevel programming problem, Journal of Optimization Theory and Applications, v.68 n.2, p.371-378, Feb. 1991 Contributor: Alex Meeraus and Jan-H. Jagla, December 2009 \$offtext *Solution of problem 9.1.5 on the web scalar x_l / 1 / y1_l / 0 / y2_l / 0 / tol / 1e-6 /; variables z, z_in; positive variable x, y1, y2; equations ob, ob_in, c1, c2, c3; ob.. - x + 10*y1 - y2 =e= z; ob_in .. - y1 - y2 =e= z_in; c1.. x + y1 =l= 1; c2.. x + y2 =l= 1; c3.. y1 + y2 =l= 1; model bilevel / all /; \$echo bilevel x min z_in * ob_in c1 c2 c3 > "%emp.info%" *Start from reported solution x.l = x_l ; y1.l = y1_l; y2.l = y2_l; solve bilevel using EMP minimizing z; abort\$( (abs( x.l - x_l) > tol) or (abs(y1.l - y1_l) > tol) or (abs(y2.l - y2_l) > tol) ) 'Deviated from reported solution';