Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 68, Issue 12, Pages 3771-3779Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2007.04.018
Keywords
nonlinear multiobjective optimization; weak Pareto solution; weak sharp minima; normed space
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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. (C) 2007 Elsevier Ltd. All rights reserved.
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