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The term Lagrangian refers to any of several mathematical concepts developed by Joseph Louis Lagrange:
- In optimization theory, the Lagrangian function is used to solve constrained minimization problems; see Lagrange multipliers.
- The method of approximating a difficult constrained problem with an easier problem having an enlarged feasible set (allowing but penalizing some violation of constraints), is called Lagrangian relaxation.
- The problem of maximizing the value of the Lagrangian function, in terms of the Lagrange-multiplier variable, is the Lagrangian dual problem.
- In the calculus of variations, the Lagrangian is a functional whose extrema are to be determined.
- In symplectic geometry, a Lagrangian submanifold is a special class of submanifolds, with dimension half the dimension of the ambient space and where the symplectic form vanishes identically.
- Lagrangian system
- Lagrangian mechanics is a formulation of classical mechanics for particles, in which the Lagrangian summarizes the dynamics of a system.
- Lagrangian (field theory) is a formulation of classical field theory for continua and fields, in which the Lagrangian density (often simply called the Lagrangian) summarizes the dynamics of a system.
- In orbital mechanics, the Lagrangian points are stable and meta-stable points of a two body system.
- In continuum mechanics, Lagrangian coordinates are a way of describing the motions of particles of a solid or fluid.
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