classification of optimization problem

Question

When I do some exercises of optimization, I always run into some defined problems like QP (quadratic programming), CCLP(chance- constrained linear programming) and so on. I want to know how to find the standard of classifying different optimization problems and also why the following problem is called NP:

$$\min \sum\limits_{i=1}^{n}\frac{c_i}{x_i^p}$$ $$s.t. x_i > 0, \forall i = 1, 2, 3, ..., n$$ $$\sum\limits_{i=1}^{n}x_{i}^{p} \leq 1 $$

Is there any related materials about this problem? I cannot find any information about this kind of problems since when I search "NP", mosttime it means non-polynomial.

Answer 1

I would call this NLP (nonlinear programming) because it has a nonlinear objective or because it has a nonlinear constraint. See https://or.stackexchange.com/questions/865/what-are-common-and-not-so-common-abbreviations-in-operations-research