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A class of polynomial primal-dual interior-point algorithms for semidefinite optimization 认领 引用 被引量：6
1
作者 王国强 白延琴 《Journal of Shanghai University(English Edition)》 2006年第3期198-207,共10页
In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to... In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity ＂analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O（qn^（p＋q/q（P＋1）log n/ε and O（q^2√n）log n/ε,respectlvely. 展开更多
关键词 semidefinite optimization （SDO） primal-dual interior-point methods large- and small-update methods polynomial complexity
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A new primal-dual path-following interior-point algorithm for linearly constrained convex optimization 认领 引用 被引量：1
2
作者 张敏 白延琴 王国强 《Journal of Shanghai University(English Edition)》 2008年第6期475-480,共6页
In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions a... In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε). 展开更多
关键词 linearly constrained convex optimization （LCCO） interior-point algorithm small-update method polynomial complexity
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Primal-Dual Interior-Point Algorithms with Dynamic Step-Size Based on Kernel Functions for Linear Programming 认领 引用 被引量：3
3
作者 钱忠根 白延琴 《Journal of Shanghai University(English Edition)》 2005年第5期391-396,共6页
In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming （LP） problems. The algorithms are based on a few kernel functions, including both serf-regular functio... In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming （LP） problems. The algorithms are based on a few kernel functions, including both serf-regular functions and non-serf-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynaraic step size are more efficient than those with fixed step size. 展开更多
关键词 linear programming （LP） interior-point algorithm small-update method large-update method.
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An Efficient Hyperbolic Kernel Function Yielding the Best Known Iteration Bounds for Linear Programming 认领 引用
4
作者 Imene TOUIL Wided CHIKOUCHE +1 位作者 Djamel BENTERKI Amina ZERARI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2025年第1期133-151,共19页
Interior-point methods(IPMs) for linear programming(LP) are generally based on the logarithmic barrier function. Peng et al.(J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functi... Interior-point methods(IPMs) for linear programming(LP) are generally based on the logarithmic barrier function. Peng et al.(J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functions(KFs) for solving IPMs. These KFs are strongly convex and smoothly coercive on their domains.Later, Bai et al.(SIAM J. Optim. 15(1): 101–128, 2004) introduced the first KF with a trigonometric barrier term. Since then, no new type of KFs were proposed until 2020, when Touil and Chikouche(Filomat. 34(12):3957–3969, 2020;Acta Math. Sin.(Engl. Ser.), 38(1): 44–67, 2022) introduced the first hyperbolic KFs for semidefinite program(ming(SD)P). They( establishe)d that the iteration complexities of algorithms based on their proposed KFs are O(n2/3log(n/ε) and O(n3/4log(n/ε)) for large-update methods, respectively. The aim of this work is to improve the complexity result for large-update method. In fact, we present a new parametric KF with a hyperbolic barrier term. By simple tools, we show that the worst-case iteration complexity of our algorithm for the large-update method is O(√n log n log(n/ε)) iterations. This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of KFs.The algorithm based on the proposed KF has been tested. Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results. 展开更多
关键词 linear programming primal-dual interior-point methods kernel functions complexity analysis large and small-update methods
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Primal-dual Interior-point Algorithms for Second-order Cone Optimization Based on a New Parametric Kernel Function 认领 引用 被引量：10
5
作者 Yan Qin BAI Guo Qiang WANG 《Acta Mathematica Sinica,English Series》 SCIE 2007年第11期2027-2042,共16页
A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and qu... A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O（√Nlog N log N/ε） for large-update methods and O（√Nlog N/ε） for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q. 展开更多
关键词 second-order cone optimization linear optimization interior-point methods large- and small-update methods polynomial-time complexity
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Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems 认领 引用 被引量：1
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作者 Imene TOUIL Wided CHIKOUCHE 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2022年第1期44-67,共24页
In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.... In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper. 展开更多
关键词 Linear Semidefinite Programming Primal-Dual Interior Point Methods Hyperbolic Kernel Function Complexity Analysis Large and small-update methods
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