V -dualities and ⊥-dualities

References

• Birkhoff , G. 1948 . Lattice theory , Vol. 25 , New York : Amer. Math. Soc. Coll. Publ . Revised
   Google Scholar
• Dolecki , S. and Kurcyusz , S. 1978 . On Φ-convexity in extremal problems . SIAM J. Control Optim , 16 : 277 – 300 .
   Web of Science ®Google Scholar
• Elster K.-H A. Wolf:Comparison between several conjugation concepts Optimal control Lecture Notes in Control and Information Sci. 95 Bulirsch R. Miele A. Stoer J. Well K.M. Springer-Verlag Berlin 1987 79 93 Heidelberg, New York, Tokyo
   Google Scholar
• Elster , K.H. and Wolf , A. 1987 . On a general concept of conjugate functions as an approach to non-convex optimization problem , Univ. of Pisa . Preprint 149
   Google Scholar
• Elster , K.H. and Wolf , A. 1988 . “ Recent results on generalized conjugate functions ” . In Trends in mathematical optimization. ISNM , Edited by: Hoffmann , K.H. , Hiriart-Urruty , J.B. , Lemaréchal , C. and Zowe , J. Vol. 84 , 67 – 78 . Basel : Birkhäuser-Verlag . Boston
   Google Scholar
• Evers , J.J.M. and Van Maaren , H. 1985 . Duality principles in mathematics and their relations to conjugate functions . Nieuw Arch. Wisk , 3 : 23 – 68 .
   Google Scholar
• Flachs , J. and Pollatschek , M.A. 1979 . Duality theorems for certain programs involving minimum or maximum operations . Math. Progr , 16 : 348 – 370 .
   Web of Science ®Google Scholar
• Greenberg , H.J. and Pierskalla , W.P. 1973 . Quasi-conjugate functions and surrogate duality . Cahiers Centre d’Et Rech. Opér , 15 : 437 – 448 .
   Google Scholar
• Martínez-Legaz , J.E. 1988 . Quasiconvex duality theory by generalized conjugation methods . Optimization , 19 : 603 – 652 .
   Google Scholar
• Martinez-Legaz , J.-E. Generalized conjugation and related topics . Proc. Internal. Workshop on Generalized concavity, fractional programming and economic applications . 30 May 1988 , Pisa. Jun 1 (to appear)
   Google Scholar
• Martínez-Legaz , J.E. and Singer , I. 1990 . Dualities between complete lattices . Optimization , 21 ( 4 ) : 481 – 508 .
   Google Scholar
• Martinez-Legaz J.-E Singer I. Some characterizations of surrogate dual problems submitted
   Google Scholar
• Moreau , J.J. 1966 . Fonctionnelles convexes , Vol. 2 , Paris : Semin. Eq. Deriv. Part. College de France . 1967
   Google Scholar
• Moreau , J.J. 1970 . Inf-convolution, sous-additivite, convexite des fonctions numeriques . J. Math. Pures Appl , 49 : 109 – 154 .
   Google Scholar
• Ore , O. 1962 . Theory of graphs , Vol. 38 , Providence : Amer. Math. Soc. Coll. Publ .
   Google Scholar
• Pickert , G. 1952 . Bemerkungen iiber GALOIS-Verbindungen . Arch. Mat , 3 : 285 – 289 .
   Google Scholar
• Plastria , F. 1985 . Lower subdifferentiable functions and their minimization by cutting planes . J. Optim. Theory Appl , 46 : 37 – 53 .
   Web of Science ®Google Scholar
• Singer , I. Pseudo-conjugate functionals and pseudo-duality . Mathematical methods in operations research (invited lectures presented at the Internat. Confer, in Sofia . Nov 1980 . pp. 115 – 134 . Sofia : Publ. House Bulgarian Acad. Sci .
   Google Scholar
• Singer , I. 1983 . The lower semi-continuous quasi-convex hull as a normalized second conjugate . Nonlinear Anal. Theory Methods Appl , 7 : 1115 – 1121 .
   Web of Science ®Google Scholar
• Singer , I. 1983 . Surrogate conjugate functionals and surrogate convexity . Applicable Anal , 16 : 291 – 327 .
   Web of Science ®Google Scholar
• Singer I. Conjugation operators Selected topics in operations research and mathematical economics Hammer G. Pallaschke D. Springer-Verlag Berlin 1984 226 80 97 Lecture Notes in Econ. and Math. Systems Heidelberg, New York, Tokyo
   Google Scholar
• Singer , I. 1984 . Conjugate functionals and level sets . Nonlinear Anal. Theory Methods Appl , 8 : 313 – 320 .
   Web of Science ®Google Scholar
• Singer , I. 1986 . Some relations between dualities, polarities, coupling functionals and conjugations . J. Math. Anal. Appl , 115 : 1 – 22 .
   Web of Science ®Google Scholar
• Singer , I. 1987 . Infimal generators and dualities between complete lattices . Ann. Mat. Pura Appl , 148 ( 4 ) : 289 – 358 .
   Web of Science ®Google Scholar
• Volle , M. 1986 . Contributions à la dualite en optimisation et a Fepi-convergcnce , Univ, de Pau . These
   Google Scholar