* System of nonlinear equations * Himmelblau function (Reklaitis and Ragdell, 1983) * 9 known solutions VARIABLES x1 x2 s objval objective function variable; FREE VARIABLES objval; EQUATIONS f Objective function h1p h1m h2p h2m ; f .. objval =e=s; h1p .. -42 * x1 - s + 2 * POWER(x2,2) + 4 * x1 * x2 + 4 * POWER(x1,3) =l= 14; h2p .. -26 * x2 - s + 2 * POWER(x1,2) + 4 * x1 * x2 + 4 * POWER(x2,3) =l= 22; h1m .. 42 * x1 - s - 2 * POWER(x2,2) - 4 * x1 * x2 - 4 * POWER(x1,3) =l= -14; h2m .. 26 * x2 - s - 2 * POWER(x1,2) - 4 * x1 * x2 - 4 * POWER(x2,3) =l= -22; * Bounds x1.LO = -5; x1.UP = 5; x2.LO = -5; x2.UP = 5; MODEL test /ALL/; SOLVE test USING NLP MINIMIZING objval;