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On Semi-Infinite Optimization Problems with Vanishing Constraints Involving Interval-Valued Functions

Author

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  • Bhuwan Chandra Joshi

    (Department of Mathematics, School of Advanced Engineering, UPES, Dehradun 248007, India)

  • Murari Kumar Roy

    (Department of Mathematics, Graphic Era (Deemed to Be University), Dehradun 248002, India)

  • Abdelouahed Hamdi

    (Mathematics Program, Department of Mathematics and Statistics, College of Arts and Sciences, Qatar University, Doha P.O. Box 2713, Qatar)

Abstract

In this paper, we examine a semi-infinite interval-valued optimization problem with vanishing constraints (SIVOPVC) that lacks differentiability and involves constraints that tend to vanish. We give definitions of generalized convex functions along with supportive examples. We investigate duality theorems for the SIVOPVC problem. We establish these theorems by creating duality models, which establish a relationship between SIVOPVC and its corresponding dual models, assuming generalized convexity conditions. Some examples are also given to illustrate the results.

Suggested Citation

  • Bhuwan Chandra Joshi & Murari Kumar Roy & Abdelouahed Hamdi, 2024. "On Semi-Infinite Optimization Problems with Vanishing Constraints Involving Interval-Valued Functions," Mathematics, MDPI, vol. 12(7), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1008-:d:1365490
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    References listed on IDEAS

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    1. S. K. Mishra & Vinay Singh & Vivek Laha, 2016. "On duality for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 243(1), pages 249-272, August.
    2. H. C. Wu, 2008. "Wolfe Duality for Interval-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 497-509, September.
    3. G.H. Lin & M. Fukushima, 2003. "Some Exact Penalty Results for Nonlinear Programs and Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 67-80, July.
    4. Sajjad Kazemi & Nader Kanzi, 2018. "Constraint Qualifications and Stationary Conditions for Mathematical Programming with Non-differentiable Vanishing Constraints," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 800-819, December.
    5. M. Soleimani-damaneh, 2012. "Characterizations and applications of generalized invexity and monotonicity in Asplund spaces," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 592-613, October.
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