Characterization Theorems Associated with (F, ρ)-Convex and (F, ρ)-Pseudoconvex Functions

REFERENCES

• T. Antczak and K. Kisiel ( 2006 ). Strict minimizers of order m in nonsmooth optimization problems . Commentationes Mathematicae Universitatis Carolinae 47 ( 2 ): 213 – 232 .
   Google Scholar
• D. Bhatia and P. Jain (1994). Generalized (F, ρ)-convexity and duality for nonsmooth multi-objective programs. Optimization 31:153–164.
   Google Scholar
• A. Ben-Israel and B. Mond ( 1986 ). What is invexity? J. Australian Math. Soc. Ser. B 28 ( 1 – 9 ).
   Google Scholar
• F.E. Caprari ( 2003 ). ρ-invex functions and (F, ρ) convex functions: properties and equivalences . Optimization 52 : 65 – 74 .
   Web of Science ®Google Scholar
• F.H. Clarke ( 1983 ). Optimization and Nonsmooth Analysis . Wiley Interscience , New York .
   Google Scholar
• F.H. Clarke , Yu.S. Ledyaev , R.J. Stern , and P.R. Wolenski ( 1997 ). Nonsmooth Analysis and Control Theory . Springer , Berlin .
   Google Scholar
• B.D. Craven ( 1981 ). Invex functions and constrained local minima . Bull. Australian Math. Soc. 24 : 357 – 366 .
   Web of Science ®Google Scholar
• B.D. Craven and B.D. Glover ( 1985 ). Invex functions and duality . J. Australian Math. Soc. Ser. A 39 : 1 – 20 .
   Google Scholar
• R.R. Egudo and B. Mond ( 1986 ). Duality with generalized convexity . J. Australian Math. Soc. Ser. B 28 : 10 – 21 .
   Google Scholar
• M.A. Hanson ( 1981 ). On sufficiency of the Kuhn–Tucker conditions . J. Math. Anal. Appl. 80 : 545 – 550 .
   Web of Science ®Google Scholar
• M.A. Hanson and B. Mond ( 1982 ). Futher generalizations of convexity in mathematical programming . J. Information Optim. Sci. 3 : 25 – 32 .
   Google Scholar
• V. Jeyakumar ( 1985 ). Strong and weak invexity in mathematical programming . Methods Oper. Res. 55 : 109 – 125 .
   Google Scholar
• V. Jeyakumar ( 1988 ). Equivalence of a saddle-points and optima, and duality for a class of non-smooth non-convex problems . J. Math. Anal. Appl. 130 : 334 – 343 .
   Web of Science ®Google Scholar
• V. Preda ( 1992 ). On efficiency and duality for multiobjective programs . J. Math. Anal. Appl. 166 : 365 – 377 .
   Web of Science ®Google Scholar
• M.W. Reiland ( 1990 ). Nonsmooth invexity . Bull. Australian Math. Soc. 42 : 437 – 446 .
   Web of Science ®Google Scholar