×
Yang, Xin Min; Li, Duan

Semistrictly preinvex functions. (English) Zbl 0985.26007

J. Math. Anal. Appl. 258, No. 1, 287-308 (2001).
A class of functions, called semistrictly preinvex functions is defined. This is a generalization of the class of preinvex functions introduced by T. Weir and B. Mond [J. Math. Anal. Appl. 136, No. 1, 29-38 (1988; Zbl 0663.90087)] and by T. Weir and V. Jeyakumar [Bull. Aust. Math. Soc. 38, No. 2, 177-189 (1988; Zbl 0639.90082)]. It is shown that for the functions of this new class any local minimizer is global. A relationship between preinvex functions and semistrictly preinvex functions and some properties of semistrictly preinvex functions are also given.
Reviewer: Dinh The Luc (Avignon)

Cited in 3 Reviews
Cited in 27 Documents

MSC:

26B25 Convexity of real functions of several variables, generalizations
90C29 Multi-objective and goal programming
90C30 Nonlinear programming

Keywords:

preinvex function; local minimum; global minimum

Citations:

Zbl 0663.90087; Zbl 0639.90082
PDF BibTeX XML Cite
\textit{X. M. Yang} and \textit{D. Li}, J. Math. Anal. Appl. 258, No. 1, 287--308 (2001; Zbl 0985.26007)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Weir, T.; Mond, B., Pre-invex functions in multiple objective optimization, J. math. anal. appl., 136, 29-38, (1988) · Zbl 0663.90087
[2] Weir, T.; Jeyakumar, V., A class of nonconvex functions and mathematical programming, Bull. austral. math. soc., 38, 177-189, (1988) · Zbl 0639.90082
[3] Hanson, M.A., On sufficiency of the Kuhn Tucker conditions, J. math. anal. appl., 80, 545-550, (1981) · Zbl 0463.90080
[4] Craven, B.D., Invex functions and constrained local minima, Bull. austral. math. soc., 24, 357-366, (1981) · Zbl 0452.90066
[5] Craven, B.D., Invex function and duality, J. austral. math. soc. ser. A, 39, 1-20, (1985) · Zbl 0565.90064
[6] Ben-Israel, A.; Mond, B., What is invexity?, J. austral. math. soc. ser. B, 28, 1-9, (1986) · Zbl 0603.90119
[7] Pini, R., Invexity and generalized convexity, Optimization, 22, 513-525, (1991) · Zbl 0731.26009
[8] Khan, Z.A.; Hanson, M.A., On ratio invexity in mathematical programming, J. math. anal. appl., 206, 330-336, (1997) · Zbl 0872.90094
[9] Mohan, S.R.; Neogy, S.K., On invex sets and preinvex functions, J. math. anal. appl., 189, 901-908, (1995) · Zbl 0831.90097
[10] Roberts, A.W.; Varberg, D.E., Convex functions, (1973), Academic Press New York · Zbl 0289.26012
[11] Yang, X.M.; Li, D., On properties of preinvex functions, J. math. anal. appl., 256, 229-241, (2001) · Zbl 1016.90056
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.