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http://dx.doi.org/10.4134/JKMS.2003.40.2.287

ON SECOND ORDER NECESSARY OPTIMALITY CONDITIONS FOR VECTOR OPTIMIZATION PROBLEMS  

Lee, Gue-Myung (Department of Applied Mathematics Pukyung National University)
Kim, Moon-Hee (Department of Applied Mathematics Pukyung National University)
Publication Information
Journal of the Korean Mathematical Society / v.40, no.2, 2003 , pp. 287-305 More about this Journal
Abstract
Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.
Keywords
vector optimization problem; properly efficient solutions; second order necessary optimality conditions; second order contingent set; second order adjacent set; singular approximate subdifferential; (Mordukhovich) normal cone;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 4  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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1 /
[ T. Takayama ] / Mathematical Economics
2 /
[ F. H. Clarke;Yu. S. Ledyaev;R. J. Stern;P. R. Wolenski ] / Nonsmooth Analysis and Control Theory
3 Calculus for parabolic second-order derivatives /
[ D. E. Ward ] / Set-Valued Anal.   DOI
4 On Minty variational principle /
[ F. Giannessi ] / New Trends in Mathematical Programming
5 /
[ D. Blackwell;M. A. Girshick ] / Theory of Games and Statistical Decisions
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[ G. M. Lee;X. Q. Yang(et al.)(eds.) ] / Progress in Optimization
7 Generalized properly efficient solutions of vector optimization problems /
[ D. E. Ward;G. M. Lee ] / Math. Methods of Oper. Res.   DOI   ScienceOn
8 /
[ V. F. Demyanov and L. V. Vasilev ] / Nondifferentiable Optimization
9 On relations between vector optimization problems and vector variational inequalities /
[ D. E. Ward;G. M. Lee ] / J. Optim. Theory Appl.   DOI   ScienceOn
10 /
[ F. H. Clarke ] / Optimization and Nonsmooth Analysis
11 Second-order necessary conditions for optimality in nonsmooth nonlinear programming /
[ M. Studniarski ] / J. Math. Anal. Appl.   DOI
12 Optimality conditions in mathematical programming and composite optimization /
[ J. P. Penot ] / Math. Program.   DOI   ScienceOn
13 /
[ Y. Sawaragi;H. Nakayama;T. Tanino ] / Theory of Multiobjective Optimization
14 /
[ M. Zeleny ] / Multiple Criteria Decision Making
15 A chain rule for parabolic second-order epiderivatives /
[ D. E. Ward ] / Optimization   DOI
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[ B. S. Mordukhovich;D. A. Field(ed.);V. Komkov(ed.) ] / Theoretical Aspects of Industrial Design
17 Vector variational inequality and multiobjective pseudolinear programming /
[ X. Q. Yang ] / J. Optim. Theory Appl.   DOI   ScienceOn
18 /
[ J. M. Borwein;A. S. Lewis ] / Convex Analysis and Nonlinear Optimization
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[ D. E. Ward ] / Optimization   DOI
20 /
[ T. S. Ferguson ] / Mathematical Statistics, A Decision Theoretic Approach
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[ H. P. Benson ] / J. Math. Anal. Appl.
22 /
[ J. P. Aubin ] / Mathematical Methods of Game and Economic Theory
23 /
[ F. Giannessi;R. W. Cottle(ed.);F. Giannessi(ed.);J. L. Lions ] / Theorems of alternative, quadratic programs and complementarity problems in Variational Inequalities and Complementarity Problems
24 Proper efficiency and the theory of vector maximization /
[ A. M. Geoffrion ] / J. Math. Anal. Appl.   DOI
25 /
[ J. -P. Aubin;H. Frankowska ] / Set-Valued Analysis