Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem
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In this paper, we characterize the nonemptiness of the set of weak minimal elements for a nonempty subset of a linear space. Moreover, we obtain some existence results for a nonconvex set-valued optimization problem under weaker topological conditions.
KeywordsAlgebraic interior Linear space Set-valued optimization Vector closure
The authors would like to thank the associate editor and reviewers for their constructive comments, which helped us to improve the paper. We also thank Professor Nicolas Hadjisavvas and Professor Constantin Zalinescu who read our manuscript and provided us with valuable comments. The third and fourth authors were partially supported by a Grant from IPM (Nos. 96550414, 98460038).
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