In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm...In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm maintains the O (nL) ineration complexity It enjoys quadratic convergence if the optimal vertex is nondegenerate.展开更多
This paper presents a class of primal-dual path-following interior-point algorithms for symmetric cone programming(SCP)based on wide neighborhoods and new directions with a parameterθ.When the parameterθ=1,the direc...This paper presents a class of primal-dual path-following interior-point algorithms for symmetric cone programming(SCP)based on wide neighborhoods and new directions with a parameterθ.When the parameterθ=1,the direction is exactly the classical Newton direction.When the parameterθis independent of the rank of the associated Euclidean Jordan algebra,the algorithm terminates in at most O(κr logε−1)iterations,which coincides with the best known iteration bound for the classical wide neighborhood algorithms.When the parameterθ=√n/βτand Nesterov–Todd search direction is used,the algorithm has O(√r logε−1)iteration complexity,the best iteration complexity obtained so far by any interior-point method for solving SCP.To our knowledge,this is the first time that a class of interior-point algorithms including the classical wide neighborhood path-following algorithm is proposed and analyzed over symmetric cone.展开更多
redictor-corrector algorithm for linear programming, proposed by Mizuno et al. [1], becomes the best-known in the interior point methods. In this paper it is modified and then extended to solving a class of convex sep...redictor-corrector algorithm for linear programming, proposed by Mizuno et al. [1], becomes the best-known in the interior point methods. In this paper it is modified and then extended to solving a class of convex separable programming problems.展开更多
研究路径跟踪线性规划支持向量机(path following linear programming support vector machine,PF-LPSVM)分类算法,利用路径跟踪法求解线性规划的高效性,提高线性规划支持向量机在大规模数据集上的学习效率。给出线性规划支持向量机的...研究路径跟踪线性规划支持向量机(path following linear programming support vector machine,PF-LPSVM)分类算法,利用路径跟踪法求解线性规划的高效性,提高线性规划支持向量机在大规模数据集上的学习效率。给出线性规划支持向量机的模型并将其标准化,导出用路径跟踪法求解线性规划向量机的关键公式,给出完整的算法流程。在随机数据集及UCI数据集上,将所提算法与LibSVM和牛顿法线性规划向量机(Newton-LPSVM,N-LPSVM)做比较,实验结果表明,所提算法用路径跟踪法提高LPSVM的学习效率是可行的,其适用于大规模数据集的学习。展开更多
文摘In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm maintains the O (nL) ineration complexity It enjoys quadratic convergence if the optimal vertex is nondegenerate.
基金the National Natural Science Foundation of China(No.11471102)the Key Basic Research Foundation of the Higher Education Institutions of Henan Province(No.16A110012)。
文摘This paper presents a class of primal-dual path-following interior-point algorithms for symmetric cone programming(SCP)based on wide neighborhoods and new directions with a parameterθ.When the parameterθ=1,the direction is exactly the classical Newton direction.When the parameterθis independent of the rank of the associated Euclidean Jordan algebra,the algorithm terminates in at most O(κr logε−1)iterations,which coincides with the best known iteration bound for the classical wide neighborhood algorithms.When the parameterθ=√n/βτand Nesterov–Todd search direction is used,the algorithm has O(√r logε−1)iteration complexity,the best iteration complexity obtained so far by any interior-point method for solving SCP.To our knowledge,this is the first time that a class of interior-point algorithms including the classical wide neighborhood path-following algorithm is proposed and analyzed over symmetric cone.
文摘redictor-corrector algorithm for linear programming, proposed by Mizuno et al. [1], becomes the best-known in the interior point methods. In this paper it is modified and then extended to solving a class of convex separable programming problems.
文摘研究路径跟踪线性规划支持向量机(path following linear programming support vector machine,PF-LPSVM)分类算法,利用路径跟踪法求解线性规划的高效性,提高线性规划支持向量机在大规模数据集上的学习效率。给出线性规划支持向量机的模型并将其标准化,导出用路径跟踪法求解线性规划向量机的关键公式,给出完整的算法流程。在随机数据集及UCI数据集上,将所提算法与LibSVM和牛顿法线性规划向量机(Newton-LPSVM,N-LPSVM)做比较,实验结果表明,所提算法用路径跟踪法提高LPSVM的学习效率是可行的,其适用于大规模数据集的学习。
