Abstract
In this paper, we study the approximate solutions for vector optimization problem with set-valued functions. The scalar characterization is derived without imposing any convexity assumption on the objective functions. The relationships between approximate solutions and weak efficient solutions are discussed. In particular, we prove the connectedness of the set of approximate solutions under the condition that the objective functions are quasiconvex set-valued functions.
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Qiu, Q., Yang, X. Some properties of approximate solutions for vector optimization problem with set-valued functions. J Glob Optim 47, 1–12 (2010). https://doi.org/10.1007/s10898-009-9452-9
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DOI: https://doi.org/10.1007/s10898-009-9452-9
Keywords
- Vector optimization
- Set-valued function
- Scalarization
- Approximate solution
- Quasiconvex set-valued function