$title Princeton Bilevel Optimization Example 9.2.1 (FLDS921,SEQ=36) $ontext Test problem 9.3.2 in Handbook of Test Problems in Local and Global Optimization Test problem 9.2.1 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 Shimizu, K, Ishizuka, Y, and Bard, J F, Nondifferentiable and Two-Level Mathematical Programming. Kluwer Academic Publishers, 1997 Contributor: Jan-H. Jagla, January 2010 $offtext *Solution of problem 9.2.1 on the web scalar x_l / 1 / y_l / 0 / tol / 1e-6 /; variables z, z_in, y; positive variable x; equations ob, c0, c1, c2, c3, c4; ob.. sqr(x - 5) + sqr(2*y + 1) =e= z; c0.. + sqr(y) - 2*y - 1.5*x*y =e= z_in; c1.. -3*x + y =l= -3; c2.. x - 0.5*y =l= 4; c3.. x + y =l= 7; c4.. - y =l= 0; model bilevel / all /; $echo bilevel x min z_in y c0 c1 c2 c3 c4 > "%emp.info%" *Start from reported solution x.l = x_l; y.l = y_l; solve bilevel using EMP minimizing z; abort$( (abs(x.l - x_l) > tol) or (abs(y.l - y_l) > tol) ) 'Deviated from reported solution';