On the choice of parameters for power-series interior point algorithms in linear programming
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Abstract
In this paper we study higher-order interior point algorithms, especially power-series algorithms, for solving linear programming problems. Since higher-order differentials are not parameter-invariant, it is important to choose a suitable parameter for a power-series algorithm. We propose a parameter transformation to obtain a good choice of parameter, called a k-parameter, for general truncated powerseries approximations. We give a method to find a k-parameter. This method is applied to two powerseries interior point algorithms, which are built on a primal-dual algorithm and a dual algorithm, respectively. Computational results indicate that these higher-order power-series algorithms accelerate convergence compared to first-order algorithms by reducing the number of iterations. Also they demonstrate the efficiency of the k-parameter transformation to amend an unsuitable parameter in power-series algorithms. © 1995 The Mathematical Programming Society, Inc.
Keywords
Best parameter, Higher-order derivatives, k-parameter, Linear programming, Power-series interior point algorithms: Parameter transformations, Truncated power-series approximation
Source Title
Mathematical Programming
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Date
1995-01
DOI
10.1007/BF01585757
Type
Article