• Title/Summary/Keyword: Duality

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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 IN THE OPTIMAL CONTROL PROBLEMS FOR HYPERBOLIC SYSTEMS

  • Kim, Hyun-Min;Park, Jong-Yeoul;Park, Sun-Hye
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.375-383
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    • 2001
  • In this paper we deal with the duality theory of optimality for an optimal control problem governed by a class of second order evolution equations. First we establish the dual control systems by using conjugate functions and then associate them to the original optimization problem.

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Energy Optimal Transmission Strategy in CDMA System: Duality Perspective

  • Oh, Changyoon
    • Journal of the Korea Society of Computer and Information
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    • v.20 no.9
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    • pp.61-66
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    • 2015
  • We investigate rate scheduling and power allocation problem for a delay constrained CDMA systems. Specifically, we determine an energy efficient scheduling policy, while each user maintains the short term (n time slots) average throughput. More importantly, it is shown that the optimal transmission strategy for the uplink is same as that of the downlink, called uplink and downlink duality. We then examine the performance of the optimum transmission strategy for the uplink and the downlink for various system environments.

ON SURROGATE DUALITY FOR ROBUST SEMI-INFINITE OPTIMIZATION PROBLEM

  • Lee, Gue Myung;Lee, Jae Hyoung
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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    • pp.433-438
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    • 2014
  • A semi-infinite optimization problem involving a quasi-convex objective function and infinitely many convex constraint functions with data uncertainty is considered. A surrogate duality theorem for the semi-infinite optimization problem is given under a closed and convex cone constraint qualification.

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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