Semistrict \(G\)-preinvexity and its application (Q386788)

The author obtains new properties of semistrictly \(G\)-preinvex functions in the sense of \textit{H. Z. Luo} and \textit{H. X. Wu} [J. Comput. Appl. Math. 222, No. 2, 372--380 (2008; Zbl 1154.90010)]. The new properties are actually immediate consequences of the fact that semistrict \(G\)-preinvexity of a function \(f\) is equivalent to semistrict preinvexity, in the sense of \textit{X. M. Yang} and \textit{D. Li} [J. Math. Anal. Appl. 258, No. 1, 287--308 (2001; Zbl 0985.26007)], of \(G\circ f\). The author also introduces and studies a notion of strict global minimizer of order \(m\) for multiobjective optimization problems, which generalizes to the invexity setting a notion due to \textit{G. Bhatia} [J. Math. Anal. Appl. 342, No. 1, 135--145 (2008; Zbl 1144.90023)].