CENTRAL PATH Meaning and
Definition
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Central path is a term commonly used in mathematics and optimization theory to describe a trajectory or a sequence of points that lie within a feasible search region, typically defined by a set of constraints. It is particularly relevant in linear programming and convex optimization problems. The central path is characterized by its proximity to the optimal solution of the problem at hand.
In linear programming, the central path refers to a specific path within the feasible region that connects the optimal vertex with the set of feasible solutions. This path is characterized by the fact that each of its points satisfies a specific set of conditions, such as the Karush-Kuhn-Tucker (KKT) conditions. These conditions ensure that the point lies within the interior of the feasible region and that the optimality criterion is fulfilled.
The central path is often utilized as a tool in optimization algorithms to find the optimal solution of a problem. By following the trajectory of the central path, optimization algorithms can efficiently navigate through the feasible search region towards the optimal solution. The central path provides a systematic way to progressively approach the optimal solution while satisfying the problem's constraints.
Overall, the central path is a fundamental concept in optimization theory, serving as a guiding path towards the solution of mathematical programming problems. It aids in finding optimal solutions by providing a feasible trajectory that narrows down the search space progressively.
Common Misspellings for CENTRAL PATH
- central parth
- central paty
- xentral path
- ventral path
- fentral path
- dentral path
- cwntral path
- csntral path
- cdntral path
- crntral path
- c4ntral path
- c3ntral path
- cebtral path
- cemtral path
- cejtral path
- cehtral path
- cenrral path
- cenfral path
- cengral path
- cenyral path
Etymology of CENTRAL PATH
The word "central" originates from the Latin word "centralis", which is derived from the Latin noun "centrum", meaning "center". In turn, "centrum" is derived from the Greek word "kéntron", also meaning "center".
The word "path" has its roots in the Old English word "paþ", which is related to the West Germanic word "patha" and the Dutch word "pad". These are all connected to the Proto-Germanic word "paþaz", meaning "path" or "course".
When combined, "central path" refers to a route or direction that leads to the center or middle of a particular space or concept.
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