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Zbl 1191.90064
Zheng, Xi Yin; Yang, Xiao Qi
Weak sharp minima for piecewise linear multiobjective optimization in normed spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 12, A, 3771-3779 (2008). ISSN 0362-546X

Summary: In a general normed space, we consider a piecewise linear multiobjective optimization problem. We prove that a cone-convex piecewise linear multiobjective optimization problem always has a global weak sharp minimum property. By a counter example, we show that the weak sharp minimum property does not necessarily hold if the cone-convexity assumption is dropped. Moreover, under the assumption that the ordering cone is polyhedral, we prove that a (not necessarily cone-convex) piecewise linear multiobjective optimization problem always has a bounded weak sharp minimum property.

MSC 2000:: *90C29 Multi-objective programming, etc.
90C30 Nonlinear programming
90C31 Sensitivity, etc.

Keywords: nonlinear multiobjective optimization; weak Pareto solution; weak sharp minima; normed space

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Zentralblatt MATH Berlin [Germany]