• Title/Summary/Keyword: duality

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OPTIMALITY CONDITIONS AND DUALITY RESULTS OF THE NONLINEAR PROGRAMMING PROBLEMS UNDER ρ-(p, r)-INVEXITY ON DIFFERENTIABLE MANIFOLDS

  • Jana, Shreyasi;Nahak, Chandal
    • Journal of applied mathematics & informatics
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    • v.32 no.3_4
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    • pp.491-502
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    • 2014
  • In this paper, by using the notion of ${\rho}$-(p,r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. Counterexample is constructed to justify that our investigations are more general than the existing work available in the literature.

Tightening Throughput Bounds for Finite Tandem Queues via Duality

  • Tcha, Dong-Wan;Lee, Won-Taek
    • Journal of the Korean Operations Research and Management Science Society
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    • v.15 no.2
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    • pp.63-69
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    • 1990
  • This note shows that the throughput bounds for two-stage tandem queueing systems with finite buffers, obtained by the existing methods, can significantly betightened via duality.

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DUALITY AND SUFFICIENCY IN MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH INVEXITY

  • Kim, Do-Sang;Lee, Hyo-Jung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.13 no.2
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    • pp.101-108
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    • 2009
  • In this paper, we introduce generalized multiobjective fractional programming problem with two kinds of inequality constraints. Kuhn-Tucker sufficient and necessary optimality conditions are given. We formulate a generalized multiobjective dual problem and establish weak and strong duality theorems for an efficient solution under generalized convexity conditions.

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DUALITY OF WEIGHTED SUM FORMULAS OF ALTERNATING MULTIPLE T-VALUES

  • Xu, Ce
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.5
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    • pp.1261-1278
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    • 2021
  • Recently, a new kind of multiple zeta value of level two T(k) (which is called multiple T-value) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind of alternating version of multiple T-values, and study several duality formulas of weighted sum formulas about alternating multiple T-values by using the methods of iterated integral representations and series representations. Some special values of alternating multiple T-values can also be obtained.

ON DUALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS

  • Lee, Gue Myung;Kim, Moon Hee
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.4
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    • pp.723-734
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    • 2013
  • A robust optimization problem, which has a maximum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differentiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.

CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Jabeen, Z.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.75-106
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    • 2008
  • In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

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ON OPTIMALITY OF GENERALIZED OPTIMIZATION PROBLEMS ASSOCIATED WITH OPERATOR AND EXISTENCE OF (Tη; ξθ)-INVEX FUNCTIONS

  • Das, Prasanta Kumar
    • East Asian mathematical journal
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    • v.33 no.1
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    • pp.83-102
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    • 2017
  • The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

D2D Tx-Rx Pair Assignment Using Duality Concept

  • Oh, Changyoon
    • Journal of the Korea Society of Computer and Information
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    • v.24 no.5
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    • pp.19-26
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    • 2019
  • In this paper, we consider the D2D Transmitter(Tx) and Receiver(Rx) pair assignment problem in the cellular system. Sharing the resource of the cellular system, D2D users may cause interference to the cellular system, though it is beneficial to improve the D2D user Capacity. Therefore, to protect the cellular users, D2D transmit power should be carefully controlled. Previously, optimal Tx-Rx assignment to minimize the total transmit power of users was investigated. Accordingly, the iterative algorithm to find the optimum Tx-Rx asignment was obtained. In this work, we consider the case where Tx group users becomes Rx group users, and Rx group users become Tx group users. We prove that the Tx-Rx assignment problem has the duality property. We present the numerical examples that show the duality between U-link and D-link.