• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1411-1423
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• 2014

For BMO, it is well known that $VMO^{**}=BMO$. In this paper such duality results of $Q_K$-type spaces are obtained which generalize the results by M. Pavlovi$\acute{c}$ and J. Xiao.

• East Asian mathematical journal
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• v.32 no.5
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• pp.635-639
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• 2016

In this paper, we prove a sufficient optimality theorems for the problem(FP) under(V, ${\rho}$)-invexity assumption. And we give Mond-Weir type dual problem and proved weak and strong duality theorem under (V, ${\rho}$)-invexity

• 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.

• 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.

• 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.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.275-296
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• 2007

We study the self-duality operator on conic 4-manifolds. The self-duality operator can be identified as a regular singular operator in the sense of $Br\"{u}ning$ and Seeley, based on which we construct its parametrizations and closed extensions. We also compute the indexes.

• 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.

• 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.

• 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.