\$title Princeton Bilevel Optimization Example 9.2.6 (FLDS926,SEQ=41) \$ontext Test problem 9.3.7 in Handbook of Test Problems in Local and Global Optimization Test problem 9.2.6 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 Falk, J. E. and Liu, J. (1995). On bilevel programming, Part I: General nonlinear cases. Mathematical Programming, 70:47–72. Contributor: Jan-H. Jagla, January 2010 \$offtext *Solution of problem 9.2.6 on the web scalar x1_l / 0.5 / x2_l / 0.5 / y1_l / 0.5 / y2_l / 0.5 / tol / 1e-6 /; variables z, z_in, y1, y2; positive variable x1, x2; equations ob, c0, c1, c2, c3, c4; ob.. sqr(x1) - 2*x1 + sqr(x2) - 2*x2 + sqr(y1) + sqr(y2) =e= z; c0.. sqr(y1-x1) + sqr(y2-x2) =e= z_in; c1.. - y1 =l= -0.5; c2.. - y2 =l= -0.5; c3.. y1 =l= 1.5; c4.. y2 =l= 1.5; model bilevel / all /; \$echo bilevel x1 x2 min z_in * c0 c1 c2 c3 c4 > "%emp.info%" *Start from reported solution x1.l = x1_l; x2.l = x2_l; y1.l = y1_l; y2.l = y2_l; solve bilevel using EMP minimizing z; abort\$( (abs(x1.l - x1_l) > tol) or (abs(x2.l - x2_l) > tol) or (abs(y1.l - y1_l) > tol) or (abs(y2.l - y2_l) > tol) ) 'Deviated from reported solution';