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Optimality and Duality of Semi-Preinvariant Convex Multi-Objective Programming Involving Generalized ( F , α , ρ , d )- I -Type Invex Functions

Author

Listed:
  • Rongbo Wang

    (School of Mathematics and Computer Science, Yanan University, Yanan 716000, China)

  • Qiang Feng

    (School of Mathematics and Computer Science, Yanan University, Yanan 716000, China)

Abstract

Multiobjective programming refers to a mathematical problem that requires the simultaneous optimization of multiple independent yet interrelated objective functions when solving a problem. It is widely used in various fields, such as engineering design, financial investment, environmental planning, and transportation planning. Research on the theory and application of convex functions and their generalized convexity in multiobjective programming helps us understand the essence of optimization problems, and promotes the development of optimization algorithms and theories. In this paper, we firstly introduces new classes of generalized ( F , α , ρ , d ) − I functions for semi-preinvariant convex multiobjective programming. Secondly, based on these generalized functions, we derive several sufficient optimality conditions for a feasible solution to be an efficient or weakly efficient solution. Finally, we prove weak duality theorems for mixed-type duality.

Suggested Citation

  • Rongbo Wang & Qiang Feng, 2024. "Optimality and Duality of Semi-Preinvariant Convex Multi-Objective Programming Involving Generalized ( F , α , ρ , d )- I -Type Invex Functions," Mathematics, MDPI, vol. 12(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2599-:d:1461971
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    References listed on IDEAS

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    1. X. M. Yang, 2001. "On E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 699-704, June.
    2. Forget, Nicolas & Gadegaard, Sune Lauth & Nielsen, Lars Relund, 2022. "Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 302(3), pages 909-924.
    3. Z. A. Liang & H. X. Huang & P. M. Pardalos, 2001. "Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 611-619, September.
    4. Khakzad, Nima, 2023. "A goal programming approach to multi-objective optimization of firefighting strategies in the event of domino effects," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
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