I have a nonconvex optimization problem. It is actually optimizing a linear objective function over a set of linear constraints and a set of nonlinear, non convex constraints.
Is this problem NPhard? If so, haw can I prove this?
I have a nonconvex optimization problem. It is actually optimizing a linear objective function over a set of linear constraints and a set of nonlinear, non convex constraints. Is this problem NPhard? If so, haw can I prove this? 


In general, you can show that a class of problems is NPHard by taking a known NPhard problem and reducing it to a problem in your class (being careful that size of the problem does not increase too much.) Since some well known NPhard problems can easily be rewritten as nonlinear optimization problems with nonconvex constraints, the class of nonconvex nonlinear optimization problems is in general NPHard. However, this says nothing about your particular nonconvex optimization problem. 

