Multiobjective Fractional Symmetric Duality in Mathematical Programming with (C,Gf)-Invexity Assumptions

In this paper, a new class of ( C , G f ) -invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, ( F , G f ) -invexity, C-convex etc.). We consider Mond–Weir type fractional symmetric dual programs and derive duality results under ( C , G f ) -invexity assumptions. Our results generalize several known results in the literature.

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Symmetric duality in complex spaces over cones

Yugoslav journal of operations research ◽

10.2298/yjor2005015004a ◽

2021 ◽

pp. 4-4

Author(s):

Izhar Ahmad ◽

Divya Agarwal ◽

Kumar Gupta

Keyword(s):

Mathematical Programming ◽

Duality Theory ◽

Optimization Theory ◽

Second Order ◽

Symmetric Duality ◽

Polyhedral Cones ◽

Complex Spaces ◽

Duality Results ◽

Duality Relations

Duality theory plays an important role in optimization theory. It has been extensively used for many theoretical and computational problems in mathematical programming. In this paper duality results are established for first and second order Wolfe and Mond-Weir type symmetric dual programs over general polyhedral cones in complex spaces. Corresponding duality relations for nondifferentiable case are also stated. This work will also remove inconsistencies in the earlier work from the literature.

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Symmetric duality results for second-order nondifferentiable multiobjective programming problem

RAIRO - Operations Research ◽

10.1051/ro/2019044 ◽

2019 ◽

Vol 53 (2) ◽

pp. 539-558 ◽

Cited By ~ 4

Author(s):

Ramu Dubey ◽

Vishnu Narayan Mishra

Keyword(s):

Programming Problem ◽

Duality Theorem ◽

Multiobjective Programming ◽

Second Order ◽

Weak Duality ◽

Symmetric Duality ◽

Numerical Examples ◽

Duality Results ◽

Duality Relations ◽

Multiobjective Programming Problem

In this article, we study the existence of Gf-bonvex/Gf -pseudo-bonvex functions and construct various nontrivial numerical examples for the existence of such type of functions. Furthermore, we formulate Mond-Weir type second-order nondifferentiable multiobjective programming problem and give a nontrivial concrete example which justify weak duality theorem present in the paper. Next, we prove appropriate duality relations under aforesaid assumptions.

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Higher order duality for cone vector optimization problems

Asian-European Journal of Mathematics ◽

10.1142/s1793557120500205 ◽

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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Mond-Weir type second order multiobjective mixed symmetric duality with square root term under generalized univex function

An International Journal of Optimization and Control Theories & Applications (IJOCTA) ◽

10.11121/ijocta.01.2014.00175 ◽

2013 ◽

Vol 4 (1) ◽

pp. 21-33

Author(s):

Arun Kumar Tripathy

Keyword(s):

Second Order ◽

Nondifferentiable Programming ◽

Square Root ◽

Symmetric Duality ◽

New Class ◽

Duality Results ◽

Special Cases ◽

Mild Assumption ◽

Root Term

In this paper, a new class of second order (Φ,ρ)-univex and second order (Φ,ρ)-pseudo univex function are introduced with example. A pair Mond-Weir type second order mixed symmetric duality for multiobjective nondifferentiable programming is formulated and the duality results are established under the mild assumption of second order (∅,ρ) univexity and second order pseudo univexity. Special cases are discussed to show that this study extends some of the known results in related domain..

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Wolfe Type Second Order Nondifferentiable Symmetric Duality in Multiobjective Programming over Cone with Generalized (K, F)-Convexity

ISRN Applied Mathematics ◽

10.1155/2014/687917 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10

Author(s):

A. K. Tripathy

Keyword(s):

Multiobjective Programming ◽

Second Order ◽

Mixed Integer ◽

Integer Programming Problem ◽

Symmetric Duality ◽

New Class ◽

Duality Results ◽

Pseudoconvex Function ◽

Root Term ◽

Mixed Integer Programming Problem

A new class of second order (K, F) pseudoconvex function is introduced with example. A pair of Wolfe type second order nondifferentiable symmetric dual programs over arbitrary cones with square root term is formulated. The duality results are established under second order (K, F) pseudoconvexity assumption. Also a Wolfe type second order minimax mixed integer programming problem is formulated and the symmetric duality results are established under second order (K, F) pseudoconvexity assumption.

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Saddle point criteria in semi-infinite minimax fractional programming under (Φ,ρ)-invexity

Filomat ◽

10.2298/fil1709557a ◽

2017 ◽

Vol 31 (9) ◽

pp. 2557-2574 ◽

Cited By ~ 1

Author(s):

Tadeusz Antczak

Keyword(s):

Saddle Point ◽

Fractional Programming ◽

Generalized Convexity ◽

Equality Constraints ◽

New Class ◽

Minimax Fractional Programming

Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.

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Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽

10.3390/math9080894 ◽

2021 ◽

Vol 9 (8) ◽

pp. 894

Author(s):

Savin Treanţă

Keyword(s):

Multiobjective Optimization ◽

Optimization Problems ◽

Integral Functional ◽

Multiple Integral ◽

Control Problems ◽

Duality Theorems ◽

New Class ◽

Duality Results ◽

Multiobjective Optimization Problems ◽

Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

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Analysis of R-out-of-N repairable systems: the case of phase-type distributions

Advances in Applied Probability ◽

10.1239/aap/1077134467 ◽

2004 ◽

Vol 36 (1) ◽

pp. 116-138 ◽

Cited By ~ 8

Author(s):

Yonit Barron ◽

Esther Frostig ◽

Benny Levikson

Keyword(s):

Repairable System ◽

Repairable Systems ◽

Regenerative Processes ◽

Numerical Examples ◽

Independent Components ◽

Duality Results ◽

Phase Type ◽

Phase Type Distributions ◽

Two Systems ◽

Repair Facility

An R-out-of-N repairable system, consisting of N independent components, is operating if at least R components are functioning. The system fails whenever the number of good components decreases from R to R-1. A failed component is sent to a repair facility. After a failed component has been repaired it is as good as new. Formulae for the availability of the system using Markov renewal and semi-regenerative processes are derived. We assume that either the repair times of the components are generally distributed and the components' lifetimes are phase-type distributed or vice versa. Some duality results between the two systems are obtained. Numerical examples are given for several distributions of lifetimes and of repair times.

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