scholarly journals Symmetric duality in complex spaces over cones

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.

Symmetric duality results for second-order nondifferentiable multiobjective programming problem

2019 ◽  
Vol 53 (2) ◽  
pp. 539-558 ◽  
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.

scholarly journals A class of second order nondifferentiable symmetric duality relations under generalized assumptions

2020 ◽  
Vol 21 (02) ◽  
pp. 120-126 ◽  
Author(s):  
Ramu Dubey ◽  
Vandana ◽  
Vishnu Narayan Mishra ◽  
Seda Karateke
Keyword(s):  
Second Order ◽  
Symmetric Duality ◽  
Duality Relations

Duality relations for second-order programming problem under (G,αf)-bonvexity assumptions

2018 ◽  
Vol 13 (02) ◽  
pp. 2050044 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra ◽  
Puneet Tomar
Keyword(s):  
Programming Problem ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Second Order ◽  
Dual Model ◽  
Weak Duality ◽  
Numerical Examples ◽  
Duality Results ◽  
Duality Relations ◽  
Definition Of

In this paper, we introduce the definition of [Formula: see text]-bonvex/[Formula: see text]-pseudobonvex functions and to show the existence of such functions, we construct nontrivial numerical examples. In the next section, we formulate a pair of second-order symmetric dual model in optimization problem and proved the duality results under [Formula: see text]-bonvexity/[Formula: see text]-pseudobonvexity assumptions. Further, we also construct nontrivial concrete examples which justifying definitions as well as the weak duality theorem presented in the paper.

Characterizations of optimality for continuous convex mathematical programs. Part I. Linear constraints

1979 ◽  
Vol 21 (1) ◽  
pp. 37-44 ◽  
Author(s):  
C. H. Scott ◽  
T. R. Jefferson
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Linear Constraints ◽  
Lagrangian Formalism ◽  
Symmetric Duality ◽  
Mathematical Programs ◽  
Convex Functionals ◽  
Mathematical Programming Problems

AbstractRecently we have developed a completely symmetric duality theory for mathematical programming problems involving convex functionals. Here we set our theory within the framework of a Lagrangian formalism which is significantly different to the conventional Lagrangian. This allows various new characterizations of optimality.

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

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..

Wolfe-type second-order fractional symmetric duality

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Anurag Jayswal ◽  
Ioan M. Stancu-Minasian ◽  
Ashish K. Prasad
Keyword(s):  
Second Order ◽  
Mixed Integer ◽  
Symmetric Duality ◽  
Duality Results ◽  
Self Duality ◽  
Fractional Programs

AbstractIn the present paper, we examine duality results for Wolfe-type second-order fractional symmetric dual programs. These duality results are then used to investigate minimax mixed integer symmetric dual fractional programs. We also discuss self-duality results at the end.

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