Generalized monotonicity and convexity of non-differentiable functions |
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| Authors: | Liya Fan Sanyang Liu |
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| Institution: | Department of Applied Mathematics, Xidian University, Xi'an 710071, PR China |
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| Abstract: | The relationships between (strict, strong) convexity of non-differentiable functions and (strict, strong) monotonicity of set-valued mappings, and (strict, strong, sharp) pseudo convexity of non-differentiable functions and (strict, strong) pseudo monotonicity of set-valued mappings, as well as quasi convexity of non-differentiable functions and quasi monotonicity of set-valued mappings are studied in this paper. In addition, the relations between generalized convexity of non-differentiable functions and generalized co-coerciveness of set-valued mappings are also analyzed. |
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| Keywords: | Generalized convexity Generalized monotonicity Generalized co-coerciveness Clarke's generalized subdifferential mapping |
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