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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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It is well known that each kernel function defines primal-dual interior-point method (IPM). Most of polynomial-time interior-point algorithms for linear optimization (LO) are based on the logarithmic kernel function ([9]). In this paper we define new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has $\mathcal{O}(({\log}\;p)^{\frac{5}{2}}\sqrt{n}{\log}\;n\;{\log}\frac{n}{\epsilon})$ and $\mathcal{O}(q^{\frac{3}{2}}({\log}\;p)^3\sqrt{n}{\log}\;\frac{n}{\epsilon})$ iteration complexity for large- and small-update methods, respectively. These are currently the best known complexity results for such methods.
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참고문헌 (9)
참고문헌 신청
Y.Q. Bai / 2003 / A new efficient large-update primaldual interior-point method based on a nite barrier / Siam J. on Optimization 13:766~782
Y.Q. Bai / 2004 / A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization / Siam J. on Optimization 15:101~128
Y.Q. Bai / 2007 / A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms / ANZIAM J 49:259~270
Y.Q. Bai / 2009 / Primal-dual interior point algorithms for second-order cone optimization based on kernel functions / Nonlinear Analysis 70:3584~3602
N.K. Karmarkar / 1984 / A new polynomial-time algorithm for linear programming / Combinatorica 4:373~395
Y.Q. Bai / 2004 / A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization / Siam J. on Optimization 15:101~128
Y.Q. Bai / 2007 / A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms / ANZIAM J 49:259~270
Y.Q. Bai / 2009 / Primal-dual interior point algorithms for second-order cone optimization based on kernel functions / Nonlinear Analysis 70:3584~3602
N.K. Karmarkar / 1984 / A new polynomial-time algorithm for linear programming / Combinatorica 4:373~395
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