Question

Constraint combinations with equality

The differentiable functions f, g_1, …, g_11 map n-dimensional vectors x=(x_1,…,x_n) of real numbers to the real numbers. To solve a general maximisation problem with inequality constraints max f(x) s.t. g_1(x)<=0, …, g_11(x)<=0, how many equality-constrained or unconstrained maximisation problems have to be solved? Hint: recall setting some constraints to equality and omitting others (possibly all) – the answer is the number of such combinations.

Write the number of problems as a positive integer. No fractions, spaces or other symbols. Example answer (wrong): 131

Answer 1