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Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds

Author

Listed:
  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Priyanka Mishra

    (Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, Bihar, India)

  • Balendu Bhooshan Upadhyay

    (Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, Bihar, India)

Abstract

This article deals with the classes of approximate Minty- and Stampacchia-type vector variational inequalities on Hadamard manifolds and a class of nonsmooth interval-valued vector optimization problems. By using the Clarke subdifferentials, we define a new class of functions on Hadamard manifolds, namely, the geodesic L U -approximately convex functions. Under geodesic L U -approximate convexity hypothesis, we derive the relationship between the solutions of these approximate vector variational inequalities and nonsmooth interval-valued vector optimization problems. This paper extends and generalizes some existing results in the literature.

Suggested Citation

  • Savin Treanţă & Priyanka Mishra & Balendu Bhooshan Upadhyay, 2022. "Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds," Mathematics, MDPI, vol. 10(3), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:523-:d:743942
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    References listed on IDEAS

    as
    1. Yating Guo & Guoju Ye & Wei Liu & Dafang Zhao & Savin Treanţǎ, 2021. "Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems," Mathematics, MDPI, vol. 9(22), pages 1-14, November.
    2. Izhar Ahmad & Deepak Singh & Bilal Ahmad Dar, 2017. "Optimality and duality in non-differentiable interval valued multiobjective programming," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 11(3), pages 332-356.
    3. Savin Treanţă, 2021. "Duality Theorems for ( ρ , ψ , d )-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components," Mathematics, MDPI, vol. 9(8), pages 1-12, April.
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    Cited by:

    1. Arnav Ghosh & Balendu Bhooshan Upadhyay & I. M. Stancu-Minasian, 2023. "Pareto Efficiency Criteria and Duality for Multiobjective Fractional Programming Problems with Equilibrium Constraints on Hadamard Manifolds," Mathematics, MDPI, vol. 11(17), pages 1-28, August.
    2. Savin Treanţă & Balendu Bhooshan Upadhyay & Arnav Ghosh & Kamsing Nonlaopon, 2022. "Optimality Conditions for Multiobjective Mathematical Programming Problems with Equilibrium Constraints on Hadamard Manifolds," Mathematics, MDPI, vol. 10(19), pages 1-20, September.

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