A class of polynomial variable metric algorithms for linear optimization |
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Authors: | T Rapcsák T T Thang |
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Institution: | (1) Laboratory of Operations Research and Decision Systems, Computer and Automation Institute, Hungarian Academy of Sciences, P.O. Box 63, H-1518 Budapest, Hungary |
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Abstract: | In the paper, the behaviour of interior point algorithms is analyzed by using a variable metric method approach. A class of
polynomial variable metric algorithms is given achieving O ((n/β)L) iterations for solving a canonical form linear optimization problem with respect to a wide class of Riemannian metrics,
wheren is the number of dimensions and β a fixed value. It is shown that the vector fields of several interior point algorithms
for linear optimization is the negative Riemannian gradient vector field of a linear a potential or a logarithmic barrier
function for suitable Riemannian metrics.
Research Partially supported by the Hungarian National Research Foundation, Grant Nos. OTKA-T016413 and OTKA-2116. |
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Keywords: | Polynomial variable metric algorithms Interior point methods Linear optimization Riemannian metrics |
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