scholarly journals Higher order duality of multiobjective constrained ratio optimization problems

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1985-1998
Author(s):  
Arshpreet Kaur ◽  
Navdeep Kailey ◽  
M.K. Sharma
Keyword(s):  
Generalized Convexity ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Higher Order ◽  
Type I ◽  
Dual Model ◽  
Duality Theorems ◽  
Fractional Programs ◽  
Ratio Optimization ◽  
Higher Order Duality

A new concept in generalized convexity, called higher order (C,?,?,?,d) type-I functions, is introduced. To show the existence of such type of functions, we identify a function lying exclusively in the class of higher order (C,?,?,?,d) type-I functions and not in the class of (C,?,?,?,d) type-I functions already existing in the literature. Based upon the higher order (C,?,?,?,d) type-I functions, the optimality conditions for a feasible solution to be an efficient solution are derived. A higher order Schaible dual has been then formulated for nondifferentiable multiobjective fractional programs. Weak, strong and strict converse duality theorems are established for higher order Schaible dual model and relevant proofs are given under the aforesaid function.

scholarly journals Duality for Unified Higher-Order Minimax Fractional Programming with Support Function under Type-I Assumptions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1034 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra ◽  
and Rifaqat Ali
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Support Function ◽  
Final Section ◽  
Higher Order ◽  
Type I ◽  
Dual Model ◽  
Duality Theorems ◽  
Fractional Programming Problem ◽  
Minimax Fractional Programming

This article is devoted to discussing the nondifferentiable minimax fractional programming problem with type-I functions. We focus our study on a nondifferentiable minimax fractional programming problem and formulate a higher-order dual model. Next, we establish weak, strong, and strict converse duality theorems under generalized higher-order strictly pseudo ( V , α , ρ , d ) -type-I functions. In the final section, we turn our focus to study a nondifferentiable unified minimax fractional programming problem and the results obtained in this paper naturally unify. Further, we extend some previously known results on nondifferentiable minimax fractional programming in the literature.

On quasi approximate solutions for nonsmooth robust semi-infinite optimization problems

2019 ◽  
Vol 35 (3) ◽  
pp. 417-426 ◽  
Author(s):  
CHANOKSUDA KHANTREE ◽  
RABIAN WANGKEEREE ◽  
◽  
Keyword(s):  
Constraint Qualification ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Data Uncertainty ◽  
Necessary Condition ◽  
Duality Theorems ◽  
Approximate Form ◽  
Locally Lipschitz ◽  
Approximate Duality

This paper devotes to the quasi ε-solution for robust semi-infinite optimization problems (RSIP) involving a locally Lipschitz objective function and infinitely many locally Lipschitz constraint functions with data uncertainty. Under the fulfillment of robust type Guignard constraint qualification and robust type Kuhn-Tucker constraint qualification, a necessary condition for a quasi ε-solution to problem (RSIP). After introducing the generalized convexity, we give a sufficient optimality for such a quasi ε-solution to problem (RSIP). Finally, we also establish approximate duality theorems in term of Wolfe type which is formulated in approximate form.

scholarly journals A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 372
Author(s):  
Liu He ◽  
Qi-Lin Wang ◽  
Ching-Feng Wen ◽  
Xiao-Yan Zhang ◽  
Xiao-Bing Li
Keyword(s):  
Existence Theorem ◽  
Lower Order ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Strong Duality ◽  
Higher Order ◽  
Weak Duality ◽  
Duality Theorems ◽  
Benson Proper Efficiency

In this paper, we introduce the notion of higher-order weak adjacent epiderivative for a set-valued map without lower-order approximating directions and obtain existence theorem and some properties of the epiderivative. Then by virtue of the epiderivative and Benson proper efficiency, we establish the higher-order Mond-Weir type dual problem for a set-valued optimization problem and obtain the corresponding weak duality, strong duality and converse duality theorems, respectively.

scholarly journals Mixed Type Nondifferentiable Higher-Order Symmetric Duality over Cones

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 274 ◽  
Author(s):  
Izhar Ahmad ◽  
Khushboo Verma ◽  
Suliman Al-Homidan
Keyword(s):  
Mixed Type ◽  
Higher Order ◽  
Dual Model ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Self Duality ◽  
Pseudoconvex Functions

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.

Higher order duality for cone vector optimization problems

2018 ◽  
Vol 13 (01) ◽  
pp. 2050020
Author(s):  
Vivek Singh ◽  
Anurag Jayswal ◽  
S. Al-Homidan ◽  
I. Ahmad
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Strong Duality ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Support Functions ◽  
Invex Functions ◽  
New Class ◽  
Duality Results ◽  
Higher Order Duality

In this paper, we present a new class of higher order [Formula: see text]-[Formula: see text]-invex functions over cones. Further, we formulate two types of higher order dual models for a vector optimization problem over cones containing support functions in objectives as well as in constraints and establish several duality results, viz., weak and strong duality results.

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