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Volumn 134, Issue 3, 2007, Pages 499-513

Cone characterizations of approximate solutions in real vector optimization

Author keywords

Approximate solutions; Epsilon efficient solutions; Epsilon minimal elements; Translated cones

Indexed keywords

APPROXIMATE SOLUTION; EPSILON-EFFICIENT SOLUTION; EPSILON-MINIMAL ELEMENT; MINIMAL ELEMENTS; NON-DOMINATED POINTS; NONDOMINATED SOLUTIONS; REAL VECTOR; TRANSLATED CONE; VECTOR OPTIMIZATION PROBLEMS; VECTOR OPTIMIZATIONS;

EID: 36048956861     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-007-9235-8     Document Type: Article
Times cited : (25)

References (30)
  • 1
    • 23844480435 scopus 로고    scopus 로고
    • Approximation methods in multiobjective programming
    • Ruzika, S., Wiecek, M.M.: Approximation methods in multiobjective programming. J. Optim. Theory Appl. 126, 473-501 (2005)
    • (2005) J. Optim. Theory Appl. , vol.126 , pp. 473-501
    • Ruzika, S.1    Wiecek, M.M.2
  • 2
    • 0343582817 scopus 로고    scopus 로고
    • Approximately efficient solutions in vector optimization
    • Tanaka, T.: Approximately efficient solutions in vector optimization. J. Multicriteria Decis. Anal. 5, 271-278 (1996)
    • (1996) J. Multicriteria Decis. Anal. , vol.5 , pp. 271-278
    • Tanaka, T.1
  • 3
    • 0031268478 scopus 로고    scopus 로고
    • On approximate solutions in convex vector optimization
    • Deng, S.: On approximate solutions in convex vector optimization. SIAM J. Control Optim. 35, 2128-2136 (1997)
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 2128-2136
    • Deng, S.1
  • 4
    • 0035519403 scopus 로고    scopus 로고
    • On approximate minima in vector optimization
    • Dutta, J., Vetrivel, V.: On approximate minima in vector optimization. Numer. Funct. Anal. Optim. 22, 845-859 (2001)
    • (2001) Numer. Funct. Anal. Optim. , vol.22 , pp. 845-859
    • Dutta, J.1    Vetrivel, V.2
  • 5
    • 0035533689 scopus 로고    scopus 로고
    • Existence of ε-minima for vector optimization problems
    • Kazmi, K.R.: Existence of ε-minima for vector optimization problems. J. Optim. Theory Appl. 109, 667-674 (2001)
    • (2001) J. Optim. Theory Appl. , vol.109 , pp. 667-674
    • Kazmi, K.R.1
  • 6
    • 33747191993 scopus 로고    scopus 로고
    • On approximate efficiency in multiobjective programming
    • Gutiérrez, C., Jiménez, B., Novo, V.: On approximate efficiency in multiobjective programming. Math. Methods Oper. Res. 64, 165-185 (2006)
    • (2006) Math. Methods Oper. Res. , vol.64 , pp. 165-185
    • Gutiérrez, C.1    Jiménez, B.2    Novo, V.3
  • 7
    • 33747174139 scopus 로고    scopus 로고
    • On approximate solutions in vector optimization problems via scalarization
    • Gutiérrez, C., Jiménez, B., Novo, V.: On approximate solutions in vector optimization problems via scalarization. Comput. Optim. Appl. 35, 305-324 (2006)
    • (2006) Comput. Optim. Appl. , vol.35 , pp. 305-324
    • Gutiérrez, C.1    Jiménez, B.2    Novo, V.3
  • 9
    • 0021450973 scopus 로고
    • ε-Solutions in vector minimization problems
    • Loridan, P.: ε-Solutions in vector minimization problems. J. Optim. Theory Appl. 43, 265-276 (1984)
    • (1984) J. Optim. Theory Appl. , vol.43 , pp. 265-276
    • Loridan, P.1
  • 10
  • 11
    • 0344489686 scopus 로고
    • On several concepts for ε-efficiency
    • Helbig, S., Pateva, D.: On several concepts for ε-efficiency. OR Spektrum 16, 179-186 (1994)
    • (1994) OR Spektrum , vol.16 , pp. 179-186
    • Helbig, S.1    Pateva, D.2
  • 12
    • 0030268232 scopus 로고    scopus 로고
    • Epsilon approximate solutions for multiobjective programming problems
    • Yokoyama, K.: Epsilon approximate solutions for multiobjective programming problems. J. Math. Anal. Appl. 203, 142-149 (1996)
    • (1996) J. Math. Anal. Appl. , vol.203 , pp. 142-149
    • Yokoyama, K.1
  • 13
    • 22444451905 scopus 로고    scopus 로고
    • ε-Approximate solutions in multiobjective optimization
    • Li, Z., Wang, S.: ε-Approximate solutions in multiobjective optimization. Optimization 44, 161-174 (1998)
    • (1998) Optimization , vol.44 , pp. 161-174
    • Li, Z.1    Wang, S.2
  • 14
    • 33645013196 scopus 로고    scopus 로고
    • ε-Pareto optimality conditions for convex multiobjective programming via max function
    • Gutiérrez, C., Jiménez, B., Novo, V.: ε-Pareto optimality conditions for convex multiobjective programming via max function. Numer. Funct. Anal. Optim. 27, 57-70 (2006)
    • (2006) Numer. Funct. Anal. Optim. , vol.27 , pp. 57-70
    • Gutiérrez, C.1    Jiménez, B.2    Novo, V.3
  • 15
    • 0016872755 scopus 로고
    • Generalization of domination structures and nondominated solutions in multicriteria decision making
    • Bergstresser, K., Charnes, A., Yu, P.L.: Generalization of domination structures and nondominated solutions in multicriteria decision making. J. Optim. Theory Appl. 18, 3-13 (1976)
    • (1976) J. Optim. Theory Appl. , vol.18 , pp. 3-13
    • Bergstresser, K.1    Charnes, A.2    Yu, P.L.3
  • 17
    • 36049015190 scopus 로고
    • Domination sets and optimality conditions in vector optimization theory
    • in German
    • Weidner, P.: Domination sets and optimality conditions in vector optimization theory. Wiss. Z. Tech. Hochsch. Ilmenau 31, 133-146 (1985) (in German)
    • (1985) Wiss. Z. Tech. Hochsch. Ilmenau , vol.31 , pp. 133-146
    • Weidner, P.1
  • 18
    • 0016102482 scopus 로고
    • Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
    • Yu, P.L.: Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives. J. Optim. Theory Appl. 14, 319-377 (1974)
    • (1974) J. Optim. Theory Appl. , vol.14 , pp. 319-377
    • Yu, P.L.1
  • 19
    • 0004267646 scopus 로고
    • Princeton University Press Princeton
    • Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 21
    • 36049019160 scopus 로고    scopus 로고
    • Convex sets, convex cones, affine spaces and affine cones
    • Nachbin, L.: Convex sets, convex cones, affine spaces and affine cones. Rev. Colomb. Mat. 30, 1-23 (1996)
    • (1996) Rev. Colomb. Mat. , vol.30 , pp. 1-23
    • Nachbin, L.1
  • 22
    • 0037354284 scopus 로고    scopus 로고
    • Duality for Bregman projections onto translated cones and affine subspaces
    • Bauschke, H.H.: Duality for Bregman projections onto translated cones and affine subspaces. J. Approx. Theory 121, 1-12, (2003)
    • (2003) J. Approx. Theory , vol.121 , pp. 1-12
    • Bauschke, H.H.1
  • 23
    • 0034349267 scopus 로고    scopus 로고
    • Comparison of existence results for efficient points
    • Sonntag, Y., Zalinescu, C.: Comparison of existence results for efficient points. J. Optim. Theory Appl. 105, 161-188 (2000)
    • (2000) J. Optim. Theory Appl. , vol.105 , pp. 161-188
    • Sonntag, Y.1    Zalinescu, C.2
  • 25
    • 34249962010 scopus 로고
    • Complete efficiency and interdependencies between objective functions in vector optimization
    • Weidner, P.: Complete efficiency and interdependencies between objective functions in vector optimization. Z. Oper. Res. (Math. Methods Oper. Res.) 34, 91-115 (1990)
    • (1990) Z. Oper. Res. (Math. Methods Oper. Res.) , vol.34 , pp. 91-115
    • Weidner, P.1
  • 26
    • 0042377354 scopus 로고    scopus 로고
    • Order-preserving transformations and applications
    • Cambini, A., Luc, D.T., Martein, L.: Order-preserving transformations and applications. J. Optim. Theory Appl. 118, 275-293 (2003)
    • (2003) J. Optim. Theory Appl. , vol.118 , pp. 275-293
    • Cambini, A.1    Luc, D.T.2    Martein, L.3
  • 27
    • 0028257333 scopus 로고
    • Optimization over the efficient set: Four special cases
    • Benson, H.P., Sayin, S.: Optimization over the efficient set: Four special cases. J. Optim. Theory Appl. 80, 3-18 (1994)
    • (1994) J. Optim. Theory Appl. , vol.80 , pp. 3-18
    • Benson, H.P.1    Sayin, S.2
  • 28
    • 84938604116 scopus 로고    scopus 로고
    • Optimization over the efficient set: Overview
    • Yamamoto, Y.: Optimization over the efficient set: Overview. J. Glob. Optim. 22, 285-317 (2002)
    • (2002) J. Glob. Optim. , vol.22 , pp. 285-317
    • Yamamoto, Y.1
  • 29
    • 33750704919 scopus 로고    scopus 로고
    • Generating epsilon-efficient solutions in multiobjective programming
    • Engau, A., Wiecek, M.M.: Generating epsilon-efficient solutions in multiobjective programming. Eur. J. Oper. Res. 177, 1566-1579 (2007)
    • (2007) Eur. J. Oper. Res. , vol.177 , pp. 1566-1579
    • Engau, A.1    Wiecek, M.M.2
  • 30
    • 33846851465 scopus 로고    scopus 로고
    • Exact generation of epsilon-efficient solutions in multiple objective programming
    • Engau, A., Wiecek, M.M.: Exact generation of epsilon-efficient solutions in multiple objective programming. OR Spektrum 29, 335-350 (2007)
    • (2007) OR Spektrum , vol.29 , pp. 335-350
    • Engau, A.1    Wiecek, M.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.