Bulletin of the Australian Mathematical Society Bull. Austral. Math. Soc. 0004-9727 ALNBAB 2005 72 2 10.wxyz/CV72P2 http://www.austms.org.au/Publ/Bulletin/V72P2/ Xin Min Yang Ping Zhang 14 February 2006 2006 2 14 265 270 722-5129-YaZh-2005 10.wxyz/C2005V72P2p265 http://www.austms.org.au/Publ/Bulletin/V72P2/722-5129-YaZh/ Certain shortcomings are described in the second order converse duality results in the recent work of (J. Zhang and B. Mond, Bull. Austral. Math. Soc. 55(1997) 29--44). Appropriate modifications are suggested. 49N15, 49J52, 90C30 MR2183407 02246388 This research was partially supported by the National Natural Science Foundation of China (Grant 10471159), NCET and the Natural Science Foundation of Chongqing. O.L. Mangasarian J. Math. Anal. Appl. MR378829 O.L. Mangasarian; Second order and higher order duality in nonlinear programming, \textit{J. Math. Anal. Appl.} \textbf{51} (1975), pp.~607--620. B. Mond Opsearch MR441356 B. Mond; Second order duality for nonlinear programs, \textit{Opsearch} \textbf{11} (1974), pp.~90--99. B. Mond and T. Weir J. Mathematical Sciences B. Mond and T. Weir; Generalized convexity and higher order duality, \textit{J. Mathematical Sciences} \textbf{16/18} (1983), pp.~74--94. B. Mond J. Math. Anal. Appl. MR349234 B. Mond; A class of nondifferentiable mathematical programming problems, \textit{J. Math. Anal. Appl.} \textbf{46} (1974), pp.~169--174. J. Zhang and B. Mond Bull. Austral. Math. Soc. MR1428528 J. Zhang and B. Mond; Duality for a nondifferentiable programming problem, \textit{Bull. Austral. Math. Soc.} \textbf{55} (1997), pp.~29-44.