On Efficient Solutions with Trade-Offs Bounded by Given Values

REFERENCES

• H. P. Benson ( 1979 ). An improved definition of proper efficiency for vector maximization with respect to cones . J. Math. Anal. Appl. 71 : 232 – 241 .
   Web of Science ®Google Scholar
• J. M. Borwein ( 1977 ). Proper efficient points for maximization with respect to cones . SIAM J. Control Optim. 15 : 57 – 63 .
   Web of Science ®Google Scholar
• M. Ehrgott ( 2005 ). Multicriteria Optimization . Springer , Berlin .
   Google Scholar
• G. Eichfelder ( 2008 ). Adaptive Scalarization Methods in Multiobjective Optimization . Springer-Verlag , Berlin .
   Google Scholar
• A. M. Geoffrion (1968). Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22:618–630.
   Web of Science ®Google Scholar
• C. Gerth ( Tammer) and P. Weidner (1990 ). Nonconvex separation theorems and some applications in vector optimization . J. Optim. Theory Appl. 67 : 297 – 320 .
   Web of Science ®Google Scholar
• M. Henig ( 1982 ). Proper efficiency with respect to cones . J. Optim. Theory Appl. 36 ( 3 ): 387 – 407 .
   Web of Science ®Google Scholar
• J. Jahn ( 2010 ). Vector Optimization: Theory, Applications, and Extensions . Springer-Verlag , Berlin .
   Google Scholar
• J. Jahn ( 1984 ). Scalarization in vector optimization . Math. Program. A. 29 : 203 – 218 .
   Web of Science ®Google Scholar
• V. Jog , I. Kaliszewski , and W. Michalowski ( 1998 ). Using Trade-off Information in Attributes’ Investing , IIASA Interm Report, No. IR-98–19.
   Google Scholar
• I. Kaliszewski ( 1994 ). Quantitative Pareto Analysis by Cone Separation Technique . Kluwer Academic Publishers , Dordrecht .
   Google Scholar
• M. A. Krasnoselskij ( 1964 ). Positive Solutions of Operator Equations . P. Noordhoff Ltd. , Groningen .
   Google Scholar
• H. Kuhn and A. Tucker ( 1951 ). Nonlinear programming . In: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (J. Neyman , ed.). University of California Press , Berkeley , California , pp. 481 – 492 .
   Google Scholar
• D. T. Luc ( 1989 ). Theory of Vector Optimization . Lecture Notes in Economics and Mathematical Systems , Vol. 319 . Springer-Verlag , New York .
   Google Scholar
• K. Miettinen ( 1999 ). Nonlinear Multiobjective Optimization . International Series in Operations Research and Management Science , Vol. 12 . Kluwer Academic Publishers , Dordrecht .
   Google Scholar
• B. S. Mordukhovich ( 2006 ). Variational Analysis and Generalized Differentiation, II: Applications . Springer , Heidelberg .
   Google Scholar
• A. Pascoletti and P. Serafini ( 1984 ). Scalarizing vector optimization problems . J. Optim. Theory Appl. 42 : 499 – 524 .
   Web of Science ®Google Scholar
• A. M. Rubinov and R. N. Gasimov ( 2004 ). Scalarization and nonlinear scalar duality for vector optimization with preferences that are not necessarely a preorder relation . J. Global Optim. 29 : 455 – 477 .
   Web of Science ®Google Scholar
• M. Soleimani-damaneh ( 2010 ). Nonsmooth optimization using Mordukhovichs subdifferential . SIAM J. Control Optim. 48 : 3403 – 3432 .
   Web of Science ®Google Scholar
• R. E. Steuer ( 1986 ). Multiple Criteria Optimization: Theory, Computation, and Application . Wiley , New York .
   Google Scholar
• A. P. Wierzbicki ( 1986 ). On the completeness and constructiveness of parametric characterizations to vector optimization problems . OR Spectrum. 8.2 : 73 – 87 .
   Google Scholar
• A. P. Wierzbicki ( 1986 ). A methodological approach to comparing parametric characterizations of efficient solutions . In: Large-Scale Modelling and Interactive Decision Analysis ( G. Fandel , M. Grauer , A. Kurzhanski , and A. P. Wierzbicki , eds.). Vol. 273 . Springer , pp. 27 – 45 .
   Google Scholar
• A. P. Wierzbicki ( 1977 ). Basic properties of scalarizing functionals for multiobjective optimization . Mathematische Operationsforsehung und Statistik, Optimi. 8 : 55 – 60 .
   Google Scholar
• Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lnfa.
   Google Scholar