JIMO
Generalized weak sharp minima of variational inequality problems with functional constraints
Wenyan Zhang Shu Xu Shengji Li Xuexiang Huang
Journal of Industrial & Management Optimization 2013, 9(3): 621-630 doi: 10.3934/jimo.2013.9.621
In this paper, the notion of generalized weak sharp minima is introduced for variational inequality problems with functional constraints in finite-dimensional spaces by virtue of a dual gap function. Some equivalent and necessary conditions for the solution set of the variational inequality problems to be a set of generalized weak sharp minima are obtained.
keywords: Robinson's constraint qualification. dual gap function Variational inequality problems generalized weak sharp minima
JIMO
Continuity of solutions mappings of parametric set optimization problems
Jiawei Chen Guangmin Wang Xiaoqing Ou Wenyan Zhang
Journal of Industrial & Management Optimization 2017, 13(5): 1-12 doi: 10.3934/jimo.2018138

Set optimization is an indispensable part of theory and method of optimization, and has been received wide attentions due to its extensive applications in group decision and group game problems. This paper focus on the continuity of the strict (weak) minimal solution set mapping of parametric set-valued vector optimization problems with the lower set less order relation. We firstly introduce a concept of strict lower level mapping of parametric set-valued vector optimization problems. Moreover, the upper and lower semicontinuity of the strict lower level mapping are obtained under some suitable conditions. Lastly, the sufficient condition for the continuity of the strict minimal solution set mappings of parametric set optimization problems are established by a new proof method, which is different from that in [27,28].

keywords: Continuity parametric set optimization problem strict lower lever mapping lower set less order relation

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