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- W2118736602 abstract "We introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for linear optimization based on this parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive the iteration bounds for large-update methods,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi>O</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mn mathvariant=normal>2</mml:mn></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mn mathvariant=normal>3</mml:mn></mml:mrow></mml:mrow></mml:mrow></mml:msup><mml:mi>log</mml:mi><mml:mo></mml:mo><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>ε</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:math>, and small-update methods,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>O</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:msqrt><mml:mi>n</mml:mi></mml:msqrt><mml:mi>log</mml:mi><mml:mo></mml:mo><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>ε</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:math>. These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions." @default.
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- W2118736602 date "2014-01-01" @default.
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- W2118736602 title "Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term" @default.
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- W2118736602 doi "https://doi.org/10.1155/2014/710158" @default.
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