Non Linéaire Programmation (NLP) is a branch of optimisation mathématique that deals with maximizing or minimizing a non-linear fonction objectif subject to constraints that may also be non-linear. Unlike programmation linéaire, where both the objective function and the constraints are linear, NLP problems are characterized by at least one non-linear component.
NLP is widely applicable in various fields such as engineering, economics, finance, and operations research. Examples of problems that can be formulated as non-linear programming include optimisation de portefeuille, resource allocation, and structural optimization in engineering.
La general La forme d'un problème de programmation non linéaire peut être exprimée comme suit :
- Maximer ou minimiser : f(x)
- Subject to: g_i(x) ≤ 0 for i = 1, …, m (inequality constraints)
- h_j(x) = 0 for j = 1, …, p (equality constraints)
Où :
- f(x) est la fonction objectif non linéaire.
- g_i(x) sont les contraintes d'inégalité non linéaires.
- h_j(x) sont les contraintes d'égalité non linéaires.
To solve NLP problems, various algorithms are employed, including gradient-based methods (like the Lagrange multipliers), genetic algorithms, and interior-point methods. The complexity of these problems often requires specialized software and numerical techniques to find an solution optimale.
Non-linear programming is crucial in scenarios where relationships between variables are inherently non-linear, allowing for more realistic modeling of systèmes complexes par rapport à la programmation linéaire.