• 대한수학회지
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• 제44권4호
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• pp.971-985
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• 2007

A sequential optimality condition characterizing the efficient solution without any constraint qualification for an abstract convex vector optimization problem is given in sequential forms using subdifferentials and ${\epsilon}$-subdifferentials. Another sequential condition involving only the subdifferentials, but at nearby points to the efficient solution for constraints, is also derived. Moreover, we present a proposition with a sufficient condition for an efficient solution to be properly efficient, which are a generalization of the well-known Isermann result for a linear vector optimization problem. An example is given to illustrate the significance of our main results. Also, we give an example showing that the proper efficiency may not imply certain closeness assumption.

• 한국지능시스템학회논문지
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• 제20권3호
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• pp.375-379
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• 2010

Support vector machine (SVM)은 튼튼한 이론적 배경을 가지고 있고 구조적 위험을 성공적으로 최소화하기 때문에 추천가 시스템과 같은 다양한 패턴 인식 분야에서 사용되고 있다. 하지만 SVM이 초평면을 결정할 때 이상점들은 margin 손실들을 가지고 있기 때문에 이들은 초평면을 결정하는데 매우 중요한 역할을 하고 있다. 그 이유로 SVM은 이상점들에게 매우 민감한 문제점을 갖는다. 강인한 SVM을 위해 우리는 이상점들의 margin 손실의 최대치를 제한하지만 이것은 non-convex 최적화 문제를 포함한다. 따라서 본 논문에서는 non-convex 최적화 문제에 적합한 유전자 알고리즘을 이용하여 강인한 SVM을 설계하는 방법을 제안한다. 제안하는 알고리즘의 우수성을 보여주기 위하여 UCI repository에서 선택된 여러 데이터베이스들을 이용한 실험을 수행하였다.

• 한국통신학회논문지
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• 제39A권9호
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• pp.519-527
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• 2014

적응 어레이는 조향벡터를 이용하여 조향벡터 방향의 신호는 보호하면서 간섭신호를 제거한다. 조향벡터에 에러가 있으면 원하는 신호도 감쇠되어 SINR(signal-to-interference-plus-noise ratio) 성능 저하를 가져온다. 본 논문에서는 원하는 신호의 도래범위를 이용하여 조향벡터 에러에 강인한 적응 빔 형성 기법을 제시한다. 제시된 기법에서는 도래범위에서 어레이 응답벡터에 관한 상관행렬을 적분을 통해 구하고, 이 상관행렬의 고유벡터 일부를 이용하여 조향벡터를 구하기 위한 최소화 문제를 정의한다. 이 최소화 문제를 컨벡스 최적화(convex optimization)의 일종인 SDP(semidefinite program) 문제로 완화하여 효과적으로 해결한다. 시뮬레이션 결과에 따르면, 제안방식은 기존의 강인한 빔 형성 방식인 ORM(outside-range-based method), USM(uncertainty-based method)보다 우수한 SINR 성능을 나타낸다.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권6호
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• pp.2422-2443
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• 2020

This paper studies a single-user Mobile Edge Computing (MEC) system where mobile device (MD) includes an application consisting of multiple computation components or tasks with dependencies. MD can offload part of each computation-intensive latency-sensitive task to the AP integrated with MEC server. In order to accomplish the application faultlessly, we calculate out the optimal task offloading strategy in a time-division manner for a predetermined execution order under the constraints of limited computation and communication resources. The problem is formulated as an optimization problem that can minimize the energy consumption of mobile device while satisfying the constraints of computation tasks and mobile device resources. The optimization problem is equivalently transformed into solving a nonlinear equation with a linear inequality constraint by leveraging the Lagrange Multiplier method. And the proposed dual Bi-Section Search algorithm Bi-JOTD can efficiently solve the nonlinear equation. In the outer Bi-Section Search, the proposed algorithm searches for the optimal Lagrangian multiplier variable between the lower and upper boundaries. The inner Bi-Section Search achieves the Lagrangian multiplier vector corresponding to a given variable receiving from the outer layer. Numerical results demonstrate that the proposed algorithm has significant performance improvement than other baselines. The novel scheme not only reduces the difficulty of problem solving, but also obtains less energy consumption and better performance.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권1호
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• pp.1-19
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• 2020

In an underlay cognitive simultaneous wireless information and power transfer (SWIPT) network, communication from secondary user (SU) to secondary destination (SD) is accomplished with decode-and-forward (DF) relays. Multiple energy-constrained relays are assumed to harvest energy from SU via power splitting (PS) protocol and complete SU secure information transmission with beamforming. Hence, physical layer security (PLS) is investigated in cognitive SWIPT network. In order to interfere with eavesdropper and improve relay's energy efficiency, a destination-assisted jamming scheme is proposed. Namely, SD transmits artificial noise (AN) to interfere with eavesdropping, while jamming signal can also provide harvested energy to relays. Beamforming vector and power splitting ratio are jointly optimized with the objective of SU secrecy capacity maximization. We solve this non-convex optimization problem via a general two-stage procedure. Firstly, we obtain the optimal beamforming vector through semi-definite relaxation (SDR) method with a fixed power splitting ratio. Secondly, the best power splitting ratio can be obtained by one-dimensional search. We provide simulation results to verify the proposed solution. Simulation results show that the scheme achieves the maximum SD secrecy rate with appropriate selection of power splitting ratio, and the proposed scheme guarantees security in cognitive SWIPT networks.

• 한국통신학회논문지
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• 제31권9A호
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• pp.856-867
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• 2006

This paper proposes a new algorithm for opportunistic scheduling that take advantage of both multiuser diversity and power control. Motivated by the multicast RTS and priority-based CTS mechanism of OSMA protocol, we propose an opportunistic packet scheduling with power control scheme based on IEEE 802.11 MAC protocol. The scheduling scheme chooses the best candidate receiver for transmission by considering the SINR at the nodes. This mechanism ensures that the transmission would be successful. The power control algorithm on the other hand, helps reduce interference between links and could maximize spatial reuse of the bandwidth. We then formulate a convex optimization problem for minimizing power consumption and maximizing net utility of the system. We showed that if a transmission power vector satisfying the maximum transmission power and SINR constraints of all nodes exist, then there exists an optimal solution that minimizes overall transmission power and maximizes utility of the system.