Abstract
In [3, 1] gravitational methods for linear programming (LP) have been introduced. Several versions exist, the three main versions discussed there use a ball of (a): 0 radius, (b): small positive radius, and (c): the largest possible radius with the given center that will completely fit within the polytope, with the option of changing its radius as the algorithm progresses.
In versions (a), (b), after the first move, the center of the ball always remains very close to the boundary (hugs it in fact), and hence these versions behave like other boundary algorithms such as the simplex algorithm in terms of exponential complexity in the worst case [2].
Here we discuss a new gravitational method of type (c) that behaves like an interior point method.
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References
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Murty, K.G. A Gravitational Interior Point Method for LP. OPSEARCH 42, 28–36 (2005). https://doi.org/10.1007/BF03398711
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DOI: https://doi.org/10.1007/BF03398711