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논문 기본 정보
- 자료유형
- 학술대회자료
- 저자정보
- 발행연도
- 2009.11
- 수록면
- 39 - 42 (4page)
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Baes raised an open question in his monograph [1]: The theory of self-regular functions has been created for Linear Programming by Jiming Peng, Cornelius Roos, and Tam´as Terlaky [4]. They subsequently extended to Second-Order Programming and Semidefinite Programming separately, using implicitly the aforementioned construction. However, the unified treatment of this theory using the Jordan algebraic framework is not accomplished yet.
The aim of this talk is to give a partial answer for the question of Baes([1]). Following the theory of self-regular proximity functions suggested by J. Peng et al. ([3], [4]) and using the Jordan algebra theory ([1], [2]), we formulate an algorithm for a large-update primal-dual interior point method for a linear optimization problem (LOS) over a symmetric cone by using the proximity function defined by a well-known self-regular kernel function φ(t)=½(t-1/t)², obtain its new complexity analysis, and then we show that the worst-case iteration bound for
our algorithm is ο(r2/3log r/ε), where r is the rank of the underlined Euclidean Jordan algebra of LOS.
The aim of this talk is to give a partial answer for the question of Baes([1]). Following the theory of self-regular proximity functions suggested by J. Peng et al. ([3], [4]) and using the Jordan algebra theory ([1], [2]), we formulate an algorithm for a large-update primal-dual interior point method for a linear optimization problem (LOS) over a symmetric cone by using the proximity function defined by a well-known self-regular kernel function φ(t)=½(t-1/t)², obtain its new complexity analysis, and then we show that the worst-case iteration bound for
our algorithm is ο(r2/3log r/ε), where r is the rank of the underlined Euclidean Jordan algebra of LOS.
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UCI(KEPA) : I410-ECN-0101-2012-410-003696443