I am just wondering if there are any theorems about the existence of feasible solutions to the Mixed-Integer Nonlinear Programming (MINLP) problem. For example:
- Theorems about sufficient conditions ensuring the existence of feasible solutions in a MINLP problem;
- Theorems about necessary conditions ensuring the existence of feasible solutions in a MINLP problem.
Furthermore, I would really appreciate it if you could tell me the solvers (please tell me if they are free) that can find feasible solutions to a given MINLP problem.