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Primal-dual Interior-point Algorithms for second-order cone optimization Based on a New Parametric Kernel Function

Acta Mathematica Sinica,English Series 2007年第11期23卷 2027-2042页

作者： Yan Qin BAI Guo Qiang WANG Department of Mathematics College of Sciences Shanghai University Shanghai 200444 P. R. China College of Vocational Technology Shanghai University of Engineering Science Shanghai 200437 P. R. China

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.

关键词： second-order cone optimization linear optimization interior-point methods large- and small-update methods polynomial-time complexity

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A Modified and Simplified Full Nesterov–Todd Step O(N)Infeasible Interior-Point Method for second-order cone optimization

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Journal of the Operations Research Society of China 2018年第2期6卷 301-315页

作者： Behrouz Kheirfam Department of Applied Mathematics Azarbaijan Shahid Madani UniversityTabrizIran

We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et *** J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering ***,each iteration consists of only a feasibility ***,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility *** complexity result coincides with the best-known iteration bound for infeasible interior-point methods.

关键词： second-order cone optimization Infeasible interior-point method Primal-dual method Polynomial complexity

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收益率椭球分布不确定下的均值-CVaR优化研究

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Chinese Quarterly Journal of Mathematics 2023年第1期38卷 85-96页

作者：卿乃侨 School of Financial Mathematics and Statistics City University of Hong KongHong Kong 999077China

The article explores a mean-CVaR ratio model with returns distribution *** describe the uncertainty of returns distribution,a mixture ellipsoidal distribution absorbing some typical distributions such as the mixture distribution and and ellipsoidal distribution is ***,by using robust technique with some assumptions,the original robust mean-CVaR ratio model can be formulated as a second-order cone optimization model where the underlying random returns have a mixture ellipsoidal *** an illustration,the corresponding robust optimization models are applied to allocations of assets in securities *** simulations are presented to illustrate the relation between robustness and optimality and to compare mixture ellipsoidal distribution to some typical distributions as well.

关键词： Worst-case mean-CVaR ratio Mixture ellipsoidal uncertainty second-order cone optimization

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