Higher order invex functions and higher order pseudoinvex ones

References

• Roberts , AW and Varberg , DE . 1973 . Convex Functions , New York : Academic Press .
   Google Scholar
• Gilanyi , A and Pales , Z . 2008 . On convex functions of higher order . Math. Inequal. Appl. , 11 : 271 – 282 .
   Web of Science ®Google Scholar
• Ger , R and Nikodem , K . 2011 . Strongly convex functions of higher order . Nonlinear Anal. , 74 : 661 – 665 .
   Web of Science ®Google Scholar
• Ginchev , I and Ivanov , VI . 2007 . “ Higher order pseudoconvex functions ” . In Proceedings of the 8th International Symposium on Generalized Convexity/Monotonicity , Edited by: Konnov , IV , Luc , DT and Rubinov , AM . Vol. 583 , 247 – 264 . Springer, Berlin : Lecture Notes in Economics and Mathematical Systems .
   Google Scholar
• Mangasarian , OL . 1975 . Second and higher order duality in mathematical programming . J. Math. Anal. Appl. , 51 : 607 – 620 .
   Web of Science ®Google Scholar
• Ivanov , VI . 2011 . Second-order Kuhn-Tucker invex constrained problems . J. Global Optim. , 50 : 519 – 529 .
   Web of Science ®Google Scholar
• Ivanov , VI . 2012 . Second-order invex functions in nonlinear programming . Optimization , 61 : 489 – 503 .
   Web of Science ®Google Scholar
• Craven , BD and Glover , BM . 1985 . Invex functions and duality . J. Aust. Math. Soc. (Ser. A) , 39 : 1 – 20 .
   Web of Science ®Google Scholar
• Craven , BD . 2001 . “ Invexity and applications ” . In Encyclopedia of Optimization , Edited by: Floudas , CA and Pardalos , PM . Vol. 3 , 82 – 86 . Kluwer : Academic Publishers, Dordrecht .
   Google Scholar
• Hanson , MA . 1981 . On sufficiency of the Kuhn–Tucker conditions . J. Math. Anal. Appl. , 80 : 545 – 550 .
   Web of Science ®Google Scholar
• Ben-Israel , A and Mond , B . 1986 . What is invexity? . J. Aust. Math. Soc. (Ser. B) , 28 : 1 – 9 .
   Web of Science ®Google Scholar
• Yang , XM , Yang , XQ and Teo , KL . 2003 . Generalized invexity and generalized invariant monotonicity . J. Optim. Theory Appl. , 117 : 607 – 625 .
   Web of Science ®Google Scholar
• Mangasarian , OL . 1988 . A simple characterization of solution sets of convex programs . Oper. Res. Lett. , 7 : 21 – 26 .
   Web of Science ®Google Scholar
• Jeyakumar , V and Yang , XQ . 1995 . On characterizing the solution sets of pseudolinear programs . J. Optim. Theory Appl. , 87 : 747 – 755 .
   Web of Science ®Google Scholar
• Ivanov , VI . 2003 . Characterizations of the solution sets of generalized convex minimization problems . Serdica Math J. , 29 : 1 – 10 .
   Google Scholar
• Yang , XM . 2009 . On characterizing the solution set of pseudoinvex extremum problems . J. Optim. Theory Appl. , 140 : 537 – 542 .
   Web of Science ®Google Scholar
• Moham , SR and Neogy , SK . 1995 . On invex sets and preinvex functions . J. Math. Anal. Appl. , 189 : 901 – 908 .
   Web of Science ®Google Scholar
• Tanaka , Y . 1990 . Note on generalized convex functions . J. Optim. Theory Appl. , 66 : 345 – 349 .
   Web of Science ®Google Scholar
• Giorgi , G . 1990 . A note on the relationships between convexity and invexity . J. Aust. Math. Soc. (Ser. B) , 32 : 97 – 99 .
   Web of Science ®Google Scholar
• Ivanov , VI . 2010 . On a theorem due to Crouzeix and Ferland . J. Global Optim. , 46 : 31 – 47 .
   Web of Science ®Google Scholar
• Ivanov , VI . 2010 . Optimization and variational inequalities with pseudoconvex functions . J. Optim. Theory Appl. , 146 : 602 – 616 .
   Web of Science ®Google Scholar
• Pini , R . 1991 . Invexity and generalized convexity . Optimization , 21 : 513 – 525 .
   Google Scholar
• Smietanski , MJ . 2012 . A note on characterization of the solution sets to pseudolinear programming problems . Appl. Anal. , DOI: 10.1080/00036811.2011.584184. 27 June 2011
   Web of Science ®Google Scholar
• Diewert , WE , Avriel , M and Zang , I . 1981 . Nine kinds of quasiconcavity and concavity . J. Econ. Theory , 25 : 397 – 420 .
   Web of Science ®Google Scholar