Next Article in Journal
A Hybrid Approach of Interval Neutrosophic Vague Sets and DEMATEL with New Linguistic Variable
Previous Article in Journal
Alternative Hydrophobic Core in Proteins—The Effect of Specific Synergy
Open AccessArticle

Mixed Type Nondifferentiable Higher-Order Symmetric Duality over Cones

by Izhar Ahmad 1,‡, Khushboo Verma 2,‡ and Suliman Al-Homidan 1,*,‡
1
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2
Department of Applied Sciences and Humanities, Faculty of Engineering, University of Lucknow, New Campus, Lucknow 226 021, India
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(2), 274; https://doi.org/10.3390/sym12020274
Received: 29 December 2019 / Revised: 29 January 2020 / Accepted: 1 February 2020 / Published: 11 February 2020
A new mixed type nondifferentiable higher-order symmetric dual programs over cones is formulated. As of now, in the literature, either Wolfe-type or Mond–Weir-type nondifferentiable symmetric duals have been studied. However, we present a unified dual model and discuss weak, strong, and converse duality theorems for such programs under higher-order F - convexity/higher-order F - pseudoconvexity. Self-duality is also discussed. Our dual programs and results generalize some dual formulations and results appeared in the literature. Two non-trivial examples are given to show the uniqueness of higher-order F - convex/higher-order F - pseudoconvex functions and existence of higher-order symmetric dual programs.
Keywords: higher-order nondifferentiable programming; symmetric duality; self duality higher-order F-convexity/higher-order F-pseudoconvexity; duality theorems higher-order nondifferentiable programming; symmetric duality; self duality higher-order F-convexity/higher-order F-pseudoconvexity; duality theorems
MDPI and ACS Style

Ahmad, I.; Verma, K.; Al-Homidan, S. Mixed Type Nondifferentiable Higher-Order Symmetric Duality over Cones. Symmetry 2020, 12, 274.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop