메뉴 건너뛰기




Volumn 13, Issue 4, 2003, Pages 947-959

Characterizing set containments involving infinite convex constraints and reverse-convex constraints

Author keywords

Conjugate function; Infinite convex constraints; Knowledge based classifier; Reverse convex set; Set containment

Indexed keywords


EID: 0242679729     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623402401944     Document Type: Article
Times cited : (71)

References (25)
  • 1
    • 0004990788 scopus 로고    scopus 로고
    • Data mining: Overview and optimization opportunities
    • P. S. BRADLEY, U. M. FAYYAD, AND O. L. MANGASARIAN, Data mining: Overview and optimization opportunities, INFORMS J. Comput., 11 (1999), pp. 217-238.
    • (1999) INFORMS J. Comput. , vol.11 , pp. 217-238
    • Bradley, P.S.1    Fayyad, U.M.2    Mangasarian, O.L.3
  • 2
    • 27144489164 scopus 로고    scopus 로고
    • A tutorial on support vector machines for pattern recognition
    • C. J. C. BURGES, A tutorial on support vector machines for pattern recognition, Data Mining and Knowledge Discovery, 2 (1998), pp. 121-167.
    • (1998) Data Mining and Knowledge Discovery , vol.2 , pp. 121-167
    • Burges, C.J.C.1
  • 3
    • 0242420030 scopus 로고    scopus 로고
    • Knowledge-Based Support Vector Machine Classifiers
    • Data Mining Institute, Madison, WI, online from http://www.cs.wisc.edu/math-prog/techreports/
    • G. FUNG, O. L. MANGASARIAN, AND J. SHAVLIK, Knowledge-Based Support Vector Machine Classifiers, Technical Report 01-09, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, WI, 2001, ftp://ftp.cs.wisc.edu/pub/dmi/techreports/01-09.ps; also available online from http://www.cs.wisc.edu/math-prog/techreports/.
    • (2001) Technical Report 01-09
    • Fung, G.1    Mangasarian, O.L.2    Shavlik, J.3
  • 4
    • 0004177330 scopus 로고    scopus 로고
    • Linear Semi-Infinite Optimization
    • John Wiley and Sons, Chichester, UK
    • M. A. GOBERNA AND M. A. LOPEZ, Linear Semi-Infinite Optimization, Wiley Ser. Math. Methods Pract. 2, John Wiley and Sons, Chichester, UK, 1998.
    • (1998) Wiley Ser. Math. Methods Pract. , vol.2
    • Goberna, M.A.1    Lopez, M.A.2
  • 5
    • 0024113158 scopus 로고
    • Optimal value function in semi-infinite programming
    • M. A. GOBERNA AND M. A. LOPEZ, Optimal value function in semi-infinite programming, J. Optim. Theory Appl., 59 (1988), pp. 261-279.
    • (1988) J. Optim. Theory Appl. , vol.59 , pp. 261-279
    • Goberna, M.A.1    Lopez, M.A.2
  • 6
    • 0042369366 scopus 로고
    • Conditions for the closedness of the characteristic cone associated to an infinite linear system
    • E. J. Andersen and A. Philpott, eds., Springer-Verlag, Berlin
    • M. A. GOBERNA AND M. A. LOPEZ, Conditions for the closedness of the characteristic cone associated to an infinite linear system, in Infinite Programming, E. J. Andersen and A. Philpott, eds., Springer-Verlag, Berlin, 1985, pp. 16-28.
    • (1985) Infinite Programming , pp. 16-28
    • Goberna, M.A.1    Lopez, M.A.2
  • 7
    • 34250247808 scopus 로고
    • Farkas-Minkowski systems in semi-infinite programming
    • M. A. GOBERNA, M. A. LOPEZ, AND J. PASTOR, Farkas-Minkowski systems in semi-infinite programming, Appl. Math. Optim., 7 (1981), pp. 295-308.
    • (1981) Appl. Math. Optim. , vol.7 , pp. 295-308
    • Goberna, M.A.1    Lopez, M.A.2    Pastor, J.3
  • 8
    • 0030135235 scopus 로고    scopus 로고
    • Complete characterizations of global optimality for problems involving the pointwise minimum of sublinear functions
    • B. M. GLOVER, Y. ISHIZUKA, V. JEYAKUMAR, AND H. D. TUAN, Complete characterizations of global optimality for problems involving the pointwise minimum of sublinear functions, SIAM J. Optim., 6 (1996), pp. 362-372.
    • (1996) SIAM J. Optim. , vol.6 , pp. 362-372
    • Glover, B.M.1    Ishizuka, Y.2    Jeyakumar, V.3    Tuan, H.D.4
  • 9
    • 0028766961 scopus 로고
    • A Farkas lemma for difference sublinear systems and quasidifferentiable programming
    • B. M. GLOVER, V. JEYAKUMAR, AND W. OETTLI, A Farkas lemma for difference sublinear systems and quasidifferentiable programming, Math. Program., 63 (1994), pp. 109-125.
    • (1994) Math. Program. , vol.63 , pp. 109-125
    • Glover, B.M.1    Jeyakumar, V.2    Oettli, W.3
  • 10
    • 0242420026 scopus 로고    scopus 로고
    • Dual conditions characterizing optimality for convex multi-objective programs
    • B. M. GLOVER, V. JEYAKUMAR, AND A. M. RUBINOV, Dual conditions characterizing optimality for convex multi-objective programs, Math. Program., 84 (1999), pp. 201-217.
    • (1999) Math. Program. , vol.84 , pp. 201-217
    • Glover, B.M.1    Jeyakumar, V.2    Rubinov, A.M.3
  • 11
    • 0011684077 scopus 로고
    • On systems of convex inequalities
    • C.-W. HA, On systems of convex inequalities, J. Math. Anal. Appl., 68 (1979), pp. 25-34.
    • (1979) J. Math. Anal. Appl. , vol.68 , pp. 25-34
    • Ha, C.-W.1
  • 14
    • 0031532010 scopus 로고    scopus 로고
    • Asymptotic dual conditions characterizing optimality for convex programs
    • V. JEYAKUMAR, Asymptotic dual conditions characterizing optimality for convex programs, J. Optim. Theory Appl., 93 (1997), pp. 153-165.
    • (1997) J. Optim. Theory Appl. , vol.93 , pp. 153-165
    • Jeyakumar, V.1
  • 15
    • 0242587976 scopus 로고    scopus 로고
    • Farkas' Lemma: Generalizations
    • Kluwer Academic Publishers, Dordrecht, The Netherlands
    • V. JEYAKUMAR, Farkas' Lemma: Generalizations, in Encyclopedia of Optimization, Vol. 2, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 87-91.
    • (2001) Encyclopedia of Optimization , vol.2 , pp. 87-91
    • Jeyakumar, V.1
  • 16
    • 0011623193 scopus 로고
    • Nonlinear extensions of Farkas' lemma with applications to global optimization and least squares
    • V. JEYAKUMAR AND B. M. GLOVER, Nonlinear extensions of Farkas' lemma with applications to global optimization and least squares, Math. Oper. Res., 20 (1995), pp. 818-837.
    • (1995) Math. Oper. Res. , vol.20 , pp. 818-837
    • Jeyakumar, V.1    Glover, B.M.2
  • 17
    • 0001822816 scopus 로고
    • Inequality systems and optimization
    • V. JEYAKUMAR AND J. GWINNER, Inequality systems and optimization, J. Math. Anal. Appl., 159 (1991), pp. 51-71.
    • (1991) J. Math. Anal. Appl. , vol.159 , pp. 51-71
    • Jeyakumar, V.1    Gwinner, J.2
  • 19
    • 4243333160 scopus 로고    scopus 로고
    • Data Classification via Separable Convex Programming
    • University of New South Wales, Sydney, Australia
    • V. JEYAKUMAR AND B. WATERHOUSE, Data Classification via Separable Convex Programming, Appl. Math. Research Report AMR00/13, University of New South Wales, Sydney, Australia, 2000.
    • (2000) Appl. Math. Research Report , vol.AMR00-13
    • Jeyakumar, V.1    Waterhouse, B.2
  • 20
    • 0020943831 scopus 로고
    • Optimality conditions for nondifferentiable convex semi-infinite programming
    • M. A. LOPEZ AND E. VERCHER, Optimality conditions for nondifferentiable convex semi-infinite programming, Math. Programming, 27 (1983), pp. 307-319.
    • (1983) Math. Programming , vol.27 , pp. 307-319
    • Lopez, M.A.1    Vercher, E.2
  • 21
    • 0013532016 scopus 로고
    • Nonlinear Programming
    • SIAM, Philadelphia
    • O. L. MANGASARIAN, Nonlinear Programming, Classics Appl. Math. 10, SIAM, Philadelphia, 1994.
    • (1994) Classics Appl. Math. , vol.10
    • Mangasarian, O.L.1
  • 22
    • 84867927698 scopus 로고    scopus 로고
    • Set containment characterization
    • O. L. MANGASARIAN, Set containment characterization, J. Global Optim., 24 (2002), pp. 473-480.
    • (2002) J. Global Optim. , vol.24 , pp. 473-480
    • Mangasarian, O.L.1
  • 24
    • 38249027439 scopus 로고
    • Fan's theorem concerning systems of convex inequalities and its applications
    • N. SHIOJ AND W. TAKAHASHI, Fan's theorem concerning systems of convex inequalities and its applications, J. Math. Anal. Appl., 135 (1988), pp. 383-393.
    • (1988) J. Math. Anal. Appl. , vol.135 , pp. 383-393
    • Shioj, N.1    Takahashi, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.