• 충청수학회지
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• 제30권1호
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• pp.31-40
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• 2017

In this paper, we consider a nonsmooth multiobjective robust optimization problem with more than two locally Lipschitz objective functions and locally Lipschitz constraint functions in the face of data uncertainty. We prove a nonsmooth sufficient optimality theorem for a weakly robust efficient solution of the problem. We formulate a Wolfe type dual problem for the problem, and establish duality theorems which hold between the problem and its Wolfe type dual problem.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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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.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.433-455
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• 2005

Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.

• East Asian mathematical journal
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• 제17권2호
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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.

• 대한수학회지
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• 제44권2호
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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.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.139-152
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• 2003

In this paper, we characterize a vector-valued convex set function by its epigraph. The concepts of a vector-valued set function and a vector-valued concave set function we given respectively. The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced. Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.

• 한국경영과학회지
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• 제15권2호
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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.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.251-261
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• 2008

In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

• 충청수학회지
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• 제27권3호
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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.

• 한국컴퓨터정보학회논문지
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• 제24권5호
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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.