Case 1: NLP
When either the objective function or at least one of the constraints or both are non-linear it is a NLP. We use generalized reduced gradient or Quadratic Programming to solve NLP. However, NLP also requires the decision variables to be continuous
Case 2: MINLP
When either the objective function and/or at least one constraint is non-linear it is a MINLP. We use outer approximation or branch and bound to solve MINLP. However, MINLP also requires the decision variables to be both continuous and discrete(binary/integer).
Case 3: My Case
Objective function: two non-linear functions and one linear function
Decision variable: two integer variables (Bounded)
Constraint: three linear constraint (two bounding constraint and one relationship constraint)
Problem type: non-convex
Solution required: Global optimum
Will this problem require conversion to NLP or MINLP to implement the above solution methods? What exact multi-objective optimization methods can be used for my case?
Also, if the problem is converted from INLP to NLP by relaxing the decision variables to real values what exact multi-objective optimization methods can be used?