簡易檢索 / 詳目顯示

研究生: 李明晏
Li, Ming-Yen
論文名稱: 兩個非對稱錐上最佳化問題之解集合的刻畫
Characterizations of solution sets for two nonsymmetric cone programs
指導教授: 陳界山
Chen, Jein-Shan
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2017
畢業學年度: 105
語文別: 英文
論文頁數: 20
中文關鍵詞: 無中文關鍵詞
英文關鍵詞: Power cone, Exponential cone, Lagrange multipliers, K-convex mapping
DOI URL: https://doi.org/10.6345/NTNU202202841
論文種類: 學術論文
相關次數: 點閱:110下載:32
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 無中文摘要

    This paper is devoted to the characterizations of solution sets for general cone-constrained convex programming problems.In particular,when the cone reduces to two specific and nonsymmetric cone,that is,the power cone and the exponential cone,we demonstrate that the conclusion can be also verified by exploiting the structures of those two cones.

    Contents 1 Introduction 1 2 Preliminaries 2 3 MainResults 6 References 15

    [1] F. AlizadehandD.Goldfarb, Second-orderconeprogramming, Mathematical
    Programming, 95,3-52(2003).
    [2] E.D. Andersen,C.RoosandT.Terlaky, Notes ondualityinsecondorder
    and p-orderconeoptimization, Optimization,51(4),627-643(2002).
    [3] D.P. Bertsekas,A.Nedic, andA.E.Ozdaglar, Convex AnalysisandOpti-
    mization, AthenaScienti c,(2003).
    [4] J.V. BurkeandM.C.Ferris, Characterizationofsolutionsetsofconvexpro-
    grams, OperationsResearchLetters,10,57-60(1991).
    [5] J.-S. Chen, Conditions forerrorboundsandboundedlevelsetsofsomemeritfunc-
    tions forthesecond-orderconecomplementarityproblem, JournalofOptimization
    Theory andApplications,135,459-473(2007).
    [6] R. Chares, Cones andinterior-pointalgorithmsforstructuredconvexoptimization
    involving powersandexponentials, http://hdl.handle.net/2078.1/28538,(2009).
    [7] F.H. Clarke, Optimization andNonsmoothAnalysis, Wiley-Interscience,NewYork,
    NY, 1983.
    [8] H. Hoffmann, WeightedAM-GMInequalityviaElementaryMultivariableCalculus,
    The CollegeMathematicsJournal,47(1),56-58(2016).
    [9] J.-S. Chen,X.Chen,andP.Tseng, Analysisofnonsmoothvector-valuedfunc-
    tions associatedwithsecond-ordercone, MathematicalProgramming,101,95-117
    (2004).
    [10] J.-S. ChenandP.Tseng, Anunconstrainedsmoothminimizationreformula-
    tion ofsecond-orderconecomplementarityproblem, MathematicalProgramming,104,
    293-327 (2005).
    [11] S. Deng, Characterizationsofthenonemptinessandcompactnessofsolutionsets
    in convexvecteroptimization, JournalofOptimizationTheoryandApplications,96,
    123-131 (1998).
    [12] F. FacchineiandJ.-S.Pang, Finite-Dimensional VariationalInequalitiesand
    Complementarity Problems, Vol.I,NewYork,Springer,(2003).
    [13] F. GlineurandT.Terlaky, Conic formulationfor lp-norm optimization, Jour-
    nal ofOptimizationTheoryandApplications,122(2),285-307(2004).
    [14] L.T.K. Hien, DifferentialpropertiesofEuclideanprojectionontopowercone, Math-
    ematical MethodsofOperationsResearch,82(3),265-284(2015).
    [15] V. Jeyakumar,G.M.Lee,andN.Dinh, Lagrangemultiplierconditionschar-
    acterizing theoptimalsolutionsetsofcone-constrainedconvexprograms, Journalof
    Optimization TheoryandApplications,123(1),83-103(2004).
    [16] V. JeyakumarandH.Wolkowicz, GeneralizationsofSlater'sconstraintquali-
    cationforin niteconvexprograms, MathematicalProgramming,57,85-101(1992).
    [17] V. Jeyakumar,X.-Q.Yang, characterizingthesolutionsetsofpseudolinearpro-
    grams, JournalofOptimizationTheoryandApplications,87,747-755(1995).
    [18] M.S. Lobo,L.Vandenberghe,S.Boyd,H.Lebret, Applicationsofsecond-
    orderconeprogramming, LinearAlgebraanditsApplication,284,193-228(1998).
    [19] O.L. Mangasarian, A simplecharacterizationofsolutionsetsofconvexprograms,
    OperationsResearchLetters,7(1),21-26(1988).
    [20] X.-H. MiaoandJ.-S.Chen, Characterizationofsolutionsetsofcone-constrained
    convexprogrammingproblems, 9,1433-1445(2015).
    [21] S.A. Serrano, Algorithmsforunsymmetricconeoptimizationandanimplemen-
    tation forproblemswiththeexponentialcone, http://purl.stanford.edu/sn367tt9736,
    (2015).
    [22] Z.-L. WuandS.-Y.Wu, Characterizationsofthesolutionsetsofconvexpro-
    gramsandvariationalinequalityproblems, JournalofOptimizationTheoryandAp-
    plications, 130(2),339-358(2006).
    [23] G. XueandY.Ye, Anefficientalgorithmforminimizingasumofp-norms, SIAM
    Journal onOptimization,10(2),315-330(1999).
    [24] J.-C. ZhouandJ.-S.Chen, Propertiesofcircularconeandspectralfactorization
    associatedwithcircularcone, JournalofNonlinearandConvexAnalysis,14(4),807-
    816 (2013).

    下載圖示
    QR CODE