Semilocal E-convexity and semilocal E-convex programming
Qingjie Hu, Jinbao Jian, Hai-Yan Zheng, Chunming Tang · Bulletin of the Australian Mathematical Society · 2007
In this paper, a new type of generalised convexity—semilocal E-convexity is introduced by combining the concepts of the semi-E-convexity in X.S. Chen [J. Math. Anal. Appl. 275(2002), 251–262] and semilocal convexity in G.M. Ewing [SIAM. Rev. 19(1977), 202–220], and some of its basic characters are discussed. By utilising the new concepts, we derive some optimality conditions and establish some duality results for the inequality constrained optimisation problem.