On Quasiconvex Multiobjective Optimization and Variational Inequalities Using Greenberg–Pierskalla Based Generalized Subdifferentials

Shashi Kant Mishra (), Vivek Laha () and Mohd Hassan ()
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Shashi Kant Mishra: Banaras Hindu University
Vivek Laha: Banaras Hindu University
Mohd Hassan: University of Ladakh, Leh Campus

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 8, 1169-1186

Abstract: Abstract In this paper, we first characterize generalized convex functions introduced by Linh and Penot Optimization (62: 943–959, 2013) by using generalized monotonicity of the generalized subdifferentials. We use vector variational inequalities in terms of generalized subdifferentials to identify efficient solutions of a multiobjective optimization problem involving quasiconvex functions. We also establish the Minty variational principle by utilizing the mean value theorem established by Kabgani and Soleimani-damaneh (Numer. Funct. Anal. Optim 38: 1548–1563, 2017) for quasiconvex functions in terms of Greenberg–Pierskalla subdifferentials.

Keywords: Multiobjective optimization; Generalized convexity; Generalized subdifferentials; Nonsmooth analysis; Variational inequalities; Convexificators; 90C33; 52A01; 49J52; 58E17; 39B62 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02505-3

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