Lipschitz Continuity of Approximate Solution Mappings to Parametric Generalized Vector Equilibrium Problems

Yu Han ()
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Yu Han: Nanchang University

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 3, No 5, 763-793

Abstract: Abstract In this paper, we establish Lipschitz continuity of strongly efficient approximate solution mapping to parametric generalized vector equilibrium problems without using monotonicity and any information of the solution mappings. Moreover, we make a new attempt to establish Lipschitz continuity of weakly efficient approximate solution mapping and efficient approximate solution mapping to parametric generalized vector equilibrium problems by using a scalarization method and a density result, respectively. As an application of the main results, we obtain Lipschitz continuity of strongly efficient approximate solution mapping, weakly efficient approximate solution mapping and efficient approximate solution mapping to parametric vector optimization problems.

Keywords: Generalized vector equilibrium problem; Approximate solution; Scalarization; Lipschitz continuity; Vector optimization problem; 49K40; 90C31; 91B50 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1329-y

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