• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.2
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• pp.13-46
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• 2001

SDP (Semidefinite Programming), as a sort of “cone-LP”, optimizes a linear function over the intersection of an affine space and a cone that has the origin as its apex. SDP, however, has been developed in the process of searching for better solution methods for NP-hard combinatorial optimization problems. We surveyed the basic theories necessary to understand SDP researches. First, We examined SDP duality, comparing it to LP duality, which is essential for the interior point method, Second, we showed that SDP can be optimized from an interior solution in polynomial time with a desired error limit. finally, we summarized several research papers that showed SDP can improve solution methods for some combinatorial optimization problems, and explained why SDP has become one of the most important research topics in optimization. We tried to integrate SDP theories. relatively diverse and complicated. to survey research papers with our own perspective, and thus to help researcher to pursue their SDP researches in depth.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.139-147
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• 2010

A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

• 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.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.47-56
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• 2012

In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.17-28
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• 2010

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.727-753
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• 2013

In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivex functions, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-pseudosounivex functions, and ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.

• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.1-10
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• 2000

We obtain some duality results for nonsmooth multiobjective fractional programming problem under generalized invexity assumptions on the objective and constraint functions.

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
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• v.10 no.3
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• pp.85-97
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• 2015

This study examined the effects of outside directors and CEO duality on acquisition strategies and performance of Korean firms in high-technology industry. Based on the resource dependence theory, we focused on the service and resource-dependence roles from board of directors in the process of decision-making of acquisition strategies. In addition, CEO opportunism behavior rises when CEO serves as chairperson of board and induces the negative effects on acquisition performance. Specifically, we investigated the interaction effects between outside directors ratio and CEO duality. For the period of 2004 to 2012, 246 acquisitions of Korean firms in high-technology industry were analyzed to test our intended hypotheses. Our results indicate that there exist positive relationship between outside director ratio and acquisition performance for Korean high-technology firms. Negative associations prevail between CEO duality and performance consequences of acquisitions. While outside director ratio has a positive effect on acquisition performance when there is a presence of CEO duality, negative effect prevail for outside director ratio on acquisition performance in the absence of CEO duality position to hold our interaction hypothesis. The favor of dual structure can be explained with implications referring to unity of command and strong leadership driven from CEO duality that enhances the resource dependence roles of board of directors in the context of high-technology industry acquisition behaviors rendered by Korean firms.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.179-196
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• 2004

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.