Monotonicity of Primal and Dual Objective Values in Primal-dual Interior-point Algorithms | Zendy

Shinji Mizuno | Zendy; Michael J. Todd | Zendy; Levent Tunçel | Zendy

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Monotonicity of Primal and Dual Objective Values in Primal-dual Interior-point Algorithms

Author(s) -

Shinji Mizuno,

Michael J. Todd,

Levent Tunçel

Publication year - 1994

Publication title -

siam journal on optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.066

H-Index - 136

eISSN - 1095-7189

pISSN - 1052-6234

DOI - 10.1137/0804034

Subject(s) - interior point method , mathematics , monotone polygon , monotonic function , dual (grammatical number) , mathematical optimization , affine transformation , algorithm , pure mathematics , mathematical analysis , art , geometry , literature

. We study monotonicity of primal and dual objective values in the framework ofprimal-dual interior-point methods. The primal-dual affine-scaling algorithm is monotone in bothobjectives. We derive a condition under which a primal-dual interior-point algorithm with a centeringcomponent is monotone. Then we propose primal-dual algorithms that are monotone in both primaland dual objective values and achieve polynomial time bounds. We also provide some argumentsshowing that several existing...

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