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GUS-property for Lorentz cone linear complementarity problems on Hilbert spaces 被引量：3

GUS-property for Lorentz cone linear complementarity problems on Hilbert spaces
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摘要 Given a real(finite-dimensional or infinite-dimensional) Hilbert space H with a Jordan product,we consider the Lorentz cone linear complementarity problem,denoted by LCP(T,Ω,q),where T is a continuous linear operator on H,ΩH is a Lorentz cone,and q ∈ H.We investigate some conditions for which the problem concerned has a unique solution for all q ∈ H(i.e.,T has the GUS-property).Several sufficient conditions and several necessary conditions are given.In particular,we provide two suficient and necessary conditions of T having the GUS-property.Our approach is based on properties of the Jordan product and the technique from functional analysis,which is different from the pioneer works given by Gowda and Sznajder(2007) in the case of finite-dimensional spaces. Given a real（finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product,we consider the Lorentz cone linear complementarity problem,denoted by LCP（T,Ω,q）,where T is a continuous linear operator on H,ΩH is a Lorentz cone,and q ∈ H.We investigate some conditions for which the problem concerned has a unique solution for all q ∈ H（i.e.,T has the GUS-property）.Several sufficient conditions and several necessary conditions are given.In particular,we provide two suficient and necessary conditions of T having the GUS-property.Our approach is based on properties of the Jordan product and the technique from functional analysis,which is different from the pioneer works given by Gowda and Sznajder（2007） in the case of finite-dimensional spaces.
作者 MIAO XinHe HUANG ZhengHai
机构地区 Department of Mathematics
出处 《Science China Mathematics》 SCIE 2011年第6期1259-1268,共10页 中国科学：数学（英文版）
基金 supported by National Natural Science Foundation of China(Grant No. 10871144) the Natural Science Foundation of Tianjin Province (Grant No. 07JCYBJC05200)
关键词 Lorentz cone linear complementarity problem Jordan product Lorentz cone 线性互补问题 Hilbert空间 洛伦兹 GUS 财产 有限维空间 希尔伯特空间 线性算子
分类号 O221 [理学—运筹学与控制论] O177.1 [理学—基础数学]
  • 相关文献

参考文献20

  • 1Xin-he Miao,Zheng-hai Huang,Ji-ye Han.Some ω-unique and ω-ΡProperties for Linear Transformations on Hilbert Spaces[J].Acta Mathematicae Applicatae Sinica,2010,26(1):23-32. 被引量：2
  • 2黄正海,韩继业,徐大川,张立平.The non-interior continuation methods for solving the function nonlinear complementarity problem[J].Science China Mathematics,2001,44(9):1107-1114. 被引量：17
  • 3Zhenghai Huang,Jiye Han,Dachuan Xu,Liping Zhang.The non-interior continuation methods for solving theP 0 function nonlinear complementarity problem[J]. Science in China Series A: Mathematics . 2001 (9)
  • 4M. Seetharama Gowda,Thomas I. Seidman.Generalized linear complementarity problems[J]. Mathematical Programming . 1990 (1-3)
  • 5J. M. Borwein.Generalized linear complementarity problems treated without fixed-point theory[J]. Journal of Optimization Theory and Applications . 1984 (3)
  • 6Robert D. Doverspike.Some perturbation results for the Linear Complementarity Problem[J]. Mathematical Programming . 1982 (1)
  • 7S. Karamardian.The complementarity problem[J]. Mathematical Programming . 1972 (1)
  • 8S. Karamardian.Generalized complementarity problem[J]. Journal of Optimization Theory and Applications . 1971 (3)
  • 9G. J. Habetler,A. L. Price.Existence theory for generalized nonlinear complementarity problems[J]. Journal of Optimization Theory and Applications . 1971 (4)
  • 10Borwein J M,Dempster M A H.The linear order complementarity problem. Mathematics of Operations Research . 1989

二级参考文献21

  • 1Chiang, Y.Y. Merit functions on Hilbert spaces. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan, 2007 (Preprint).
  • 2Cottle, R.W., Pang, J.S., Stone, R.E. The linear complementarity problem, Academic, Boston, MA. 1992.
  • 3Dash, A.T., Nandal S. A complementarity problem in mathematical programming in Banach space. J. Math. Anal Appl., 98:318-331 (1984).
  • 4Facchinei, F., Pang, J.S. Finite-dimensional variational inequalities and complementarity problems, Vol I. Springer-Verlag, New York, 2003.
  • 5Faraut, J., Koranyi, A. Analysis on symmctric cones. Oxford Mathematical Monographs Oxford University Press, New York, 1994.
  • 6Kreyszig, E. Introductory functional anaysis with applications. Krieger Pub. Co., 1978.
  • 7Gowda,-M.S., Sznajder,-R. Some global uniqueness and solvability results for linear complementarity problems over symmetric cones. SIAM J. Optim., 18: (2007)461-481.
  • 8Gowda, M.S., Sznajder, R., Tao, J. Some P-properties for linear transformations on Euclidean Jordan algebras. Linear Algebra Appl., 393:203-232 (2004).
  • 9Han, J., Xiu, N.H., Qi, H.D. Theory and algorithms of nonlinear complementarity problems. Shanghai, Shanghai Scientific - Technical Publishers, 2006.
  • 10Huang, Z.H. Sufficient conditions on nonemptiness and boundedness of the solution set of the P0 function nonlinear complementarity problem. Oper. Res. Letters, 30:202-210 (2002).

共引文献17

同被引文献20

  • 1LIU GuoQing,LI V.Wenbo.Semiparametric bounds of mean and variance for exotic options[J].Science China Mathematics,2009,52(7):1446-1458. 被引量：2
  • 2陈星灿,MagnusFiskesjoe.胡适与安特生——兼谈胡适对20世纪前半叶中国考古学的看法[J].考古,2005(1):76-87. 被引量：8
  • 3 Facchinei F, Pang J S. Finite-Dimensional VariationalInequalities and Complementarity Problems[M]. Springer,New York, USA, 2003.
  • 4 Chiang Y Y, Pan S H, Chen J S. A merit function methodfor infinite-dimensional SOCCPs[J]. Journal of MathematicalAnalysis and Applications, 2011, 383(1): 159-178.
  • 5 Gowda M S. On the extended linear complementarityproblem[J]. Mathematical Programming, 1996, 72(1):33-50..
  • 6Han J Y, Xiu N H, Qi H D. Theory and Algorithms ofNonlinear Complementarity Problems [M]. Shanghai Scientific& Technical Publishers, Shanghai, China, 2006(inChinese).
  • 7Lobo M S, Vandenberghe L, Boyd S et al. Applications ofsecond-order cone programming [J]. Linear Algebra andIts Applications, 1998, 284(1-3): 193-228.
  • 8Alizadeh F, Goldfarb D. Second-order cone programming[J]. Mathematical Programming, 2003, 95(1): 3-51.
  • 9Miao X H, Huang Z H. The column-sufficiency and rowsufficiencyof the linear transformation on Hilbertspaces[J]. Journal of Global Optimization, 2011, 49(1):109-123.
  • 10Miao X H, Chen J S. On the Lorentz cone complementarityproblems in infinite-dimensional real Hilbert space [J].Numerical Functional Analysis and Optimization, 2011,32(5): 507-523.

引证文献3

二级引证文献23

Science China Mathematics
2011年 第6期

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