Optimality and mixed saddle point criteria in multiobjective optimization

Journal of Mathematical Analysis and Applications

Volumn 342, Issue 1, 2008, Pages 135-145

  Bhatia, Guneet ^a  

^a UNIVERSITY OF DELHI   (India)

Author keywords

Higher order strong convexity; Mixed saddle point; Partial Lagrangian; Strict minimizers

Indexed keywords

EID: 39949083224     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.11.042     Document Type: Article

References (18)

1. Rockafellar R.T. Convex Analysis (1970), Princeton Univ. Press, Princeton, NJ
2. Sawaragi Y., Nakayama H., and Tanino T. Theory of Multiobjective Optimization (1985), Academic Press, Inc., Orlando
3. Yu P.L. Multiple-Criteria Decision Making: Concepts, Techniques and Extensions (1985), Plenum Press, New York
4. Ehrgott M. Multicriteria Optimization. second ed. (2005), Springer, Berlin
5. Jahn J. Vector Optimization: Theory, Applications and Extensions (2004), Springer-Verlag, Berlin
6. Miettinen K.M. Nonlinear Multiobjective Optimization (1999), Kluwer Academic Publishers, Boston
7. Auslender A. Stability in mathematical programming with non-differentable data. SIAM J. Control Optim. 22 (1984) 239-254
8. Ward D.E. Characterizations of strict local minima and necessary conditions for weak sharp minima. J. Optim. Theory Appl. 80 (1994) 551-571
9. Jiménez B. Strict efficiency in vector optimization. J. Math. Anal. Appl. 265 (2002) 264-284
10. Jiménez B., and Novo V. First and second order sufficient conditions for strict minimality in multiobjective programming. Numer. Funct. Anal. Optim. 23 (2002) 303-322
11. Jiménez B., and Novo V. First and second order sufficient conditions for strict minimality in nonsmooth vector optimization. J. Math. Anal. Appl. 284 (2003) 496-510
12. Lin G.H., and Fukushima M. Some exact penalty results for nonlinear programs and mathematical programs with equilibrium constraints. J. Optim. Theory Appl. 118 (2003) 67-80
13. Vial J.P. Strong and weak convexity of sets and functions. Math. Oper. Res. 8 (1983) 231-259
14. Clarke F.H. Optimization and Non-Smooth Analysis (1983), Wiley-Interscience, New York
15. Chandra S., Dutta J., and Lalitha C.S. Regularity conditions and optimality in vector optimization. Numer. Funct. Anal. Optim. 25 (2004) 479-501
16. Mangasarian O.L. Nonlinear Programming. corrected reprint of the 1969 original. Classics Appl. Math. vol. 10 (1994), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
17. Li Z.F., and Wang S.Y. Lagrange multipliers and saddle points in multiobjective programming. J. Optim. Theory Appl. 83 (1984) 63-81
18. Wang S., and Li Z. Scalarization and Lagrangian duality in multiobjective optimization. Optimization 26 (1992) 315-324