求解二阶锥规划问题的VU分解方法

陆媛; 庞丽萍; 夏尊铨

doi:10.3879/j.issn.1000-0887.2010.02.014

求解二阶锥规划问题的VU分解方法

doi: 10.3879/j.issn.1000-0887.2010.02.014

大连理工大学数学科学学院,辽宁大连 116024

基金项目: 国家自然科学基金资助项目(10771026)

详细信息

作者简介:
陆媛(1981- ),女,沈阳人,博士(E-maill:uyuan626@yahoo.com.cn);庞丽萍(1968- ),女,辽宁大连人,博士,副教授(联系人.E-maill:ppang@dlu.tedu.cn).

中图分类号: O221.2；O224
计量
- 文章访问数: 2102
- HTML全文浏览量: 148
- PDF下载量: 833
- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2009-12-25
- 刊出日期: 2010-02-15

VU-Decomposition Method for a Second-Order Cone Programming Problem

School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China

摘要

摘要: 给出解决二阶锥规划(SOCP)问题的VU-分解方法.问题首先被转化为非线性规划,并给出相应的精确罚函数的Clarke次微分结构及VU-空间分解．在某种条件下,可以计算出一个二阶连续可微的轨道,进而得到目标函数f在其上的二阶展开．最后给出一个具有超线性收敛速度的概念型算法．
- 二阶锥规划 /
- 非光滑优化 /
- VU-分解 /
- U-Lagrange函数
Abstract: A VU-decomposition method for solving a second-order coneproblem was presented.First of all,this problem was trans formed into a nonlinear programming problem.Then the structure of Clarke subdifferen tial corresponding to penalty function and some results of its VU-decomposition were given.Under certain condition,a twice continuously differen tiable trajectory could be computed for yielding a second-order expansion of the objective functionf.A conceptual algorithm for solving this problem with a superlinear convergence rate was given.
- second-order cone programming /
- nonsmooth optimization /
- VU-decomposition /
- U-L agrangian

HTML全文

参考文献(14)

[1]	Alizadeh F,Schmieta S.Symmetric cones,potential reduction methods[C] Wolkowicz H,Saigal R,Vandenberghe L.Handbook of Semidefinite Programming. Boston：Kluwer,2000:195-233.
[2]	Benson H Y,Vanderbei R J.Solving problems with semidefinite and related constraints using interior point methods for nonlinear programming[J].Mathematical Programming,2003,95(2)：279-302. doi: 10.1007/s10107-002-0350-x
[3]	Fukushima M,Luo Z-Q,Tseng P.Smoothing functions for second-order-cone complementarity problems[J].SIAM Journal on Optimization,2001,12(2)：436-460.
[4]	Kanzow C,Ferenczi I,Fukushima M.Semismooth methods for linear and nonlinear second-order cone programs[R]. Technical Report 2006-005.Department of Applied Mathematics and Physics,Kyoto University,2006.
[5]	刘勇进,张立卫,王银河.线性二阶锥规划的一个光滑化方法及其收敛性[J].数学进展,2007,36(4):491-502.
[6]	Liu Y J,Zhang L W.Convergence of the augmented Lagrangian method for nonlinear optimization problems over second-order cones[J].Journal of Optimization Theory and Applications,2008,139(3)：557-575. doi: 10.1007/s10957-008-9390-6
[7]	Bai Y Q,Wang G Q.Primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function[J].Acta Mathematica Sinica,English Series,2007,23(11)：2027-2042. doi: 10.1007/s10114-007-0967-z
[8]	Lemaréchal C,Oustry F,Sagastizbal C.The U-Lagrangian of a convex function[J].Transactions of the American Mathematical Society,2000,352(2)：711-729. doi: 10.1090/S0002-9947-99-02243-6
[9]	Mifflin R,Sagastizbal C.VU-decomposition derivatives for convex max-functions[C]Tichatschke R,Théra M.Ill-Posed Variational Problems and Regularization Techniques. Lecture Notes in Economics and Mathematical Systems.Berlin Heidelberg：Springer-Verlag,1999:167-186.
[10]	Oustry F.A second-order bundle method to minimize the maximum eigenvalue function[J].Mathematical Programming,Ser A,2000,89(1):1-33. doi: 10.1007/PL00011388
[11]	Mifflin R,Sagastizbal C.On VU-theory for functions with primal-dual gradient structure[J].SIAM Journal on Optimization,2000,11(2)：547-571. doi: 10.1137/S1052623499350967
[12]	Mifflin R,Sagastizbal C.Primal-dual gradient structured functions:second-order results; links to epi-derivatives and partly smooth functions[J].SIAM Journal on Optimization,2003,13(4)：1174-1197. doi: 10.1137/S1052623402412441
[13]	Mifflin R,Sagastizbal C.Functions with primal-dual gradient structure and U-Hessians[C] Pillo Di G,Giannessi F.Nonlinear Optimization and Related Topics,Applied Optimization.B V:Kluwer Academic Publishers,2000,36:219-233.
[14]	单锋，庞丽萍，朱丽梅，等.求解一类MPEC问题的一种VU-分解方法[J].应用数学和力学，2008,29(4):483-488.