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Weak sharp minima for piecewise linear multiobjective optimization in normed spaces. (English) Zbl 1191.90064
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:
90C29Multi-objective programming; goal programming
90C30Nonlinear programming
90C31Sensitivity, stability, parametric optimization
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