Second-order conditions for constrained vector optimization problems with -stable data

作者：Ginchev Ivan^*; Guerraggio Angelo

来源：Optimization, 2011, 60(1-2): 179-199.

DOI：10.1080/02331930903578718

• vector optimization
• -stable functions
• second-order conditions

We consider the constrained vector optimization problem minC f(x), g(x) -K, where C < subset of> m and K < subset of> p are pointed closed convex cones, and f : n m and g : n p are -stable at a point x0 n. We give second-order sufficient and necessary conditions x0 to be an i-minimizer (isolated minimizer) of order two, and second-order necessary conditions x0 to be a w-minimizer (weakly efficient point). The obtained results improve the ones of Bednarik and Pastor [On second-order conditions in unconstrained optimization, Math. Program. Ser. A 113 (2008), pp. 283-298] (from unconstrained scalar problems to constrained vector problems) and Ginchev et al. [Second-order conditions in C1,1 constrained vector optimization, Math. Program. Ser. B 104 (2005), pp. 389-405], (from problems with C1,1 data to problems with -stable data). In fact, the former paper introduces and studies the notion of a -stable at a point scalar function, and shows some possible applications. Here we generalize this notion to vector functions.

• 出版日期2011