Abstract
New concepts of semistrict quasimonotonicity and strict quasimonotonicity for multivalued maps are introduced. It is shown that a locally Lipschitz map is (semi)strictly quasiconvex if and only if its Clarke subdifferential is (semi)strictly quasimonotone. Finally, an existence result for the corresponding variational inequality problem is obtained.
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Daniilidis, A., Hadjisavvas, N. Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions. Journal of Optimization Theory and Applications 102, 525–536 (1999). https://doi.org/10.1023/A:1022693822102
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DOI: https://doi.org/10.1023/A:1022693822102