• Journal of the Korean Mathematical Society
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• v.44 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.3
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• pp.375-379
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• 2010

The support vector machine (SVM) has been widely used in variety pattern recognition problems applicable to recommendation systems due to its strong theoretical foundation and excellent empirical successes. However, SVM is sensitive to the presence of outliers since outlier points can have the largest margin loss and play a critical role in determining the decision hyperplane. For robust SVM, we limit the maximum value of margin loss which includes the non-convex optimization problem. Therefore, we proposed the design method of robust SVM using genetic algorithm (GA) which can solve the non-convex optimization problem. To demonstrate the performance of the proposed method, we perform experiments on various databases selected in UCI repository.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.9
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• pp.519-527
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• 2014

Adaptive arrays can minimize contributions from interferences incident onto an sensor array while preserving a signal the direction vector of which corresponds to the array steering vector to within a scalar factor. If there exist errors in the steering vector, severe performance degradation can be caused since the desired signal is misunderstood as an interference by the array. This paper presents an adaptive beamforming method which is robust against steering vector errors, exploiting a range of the desired signal direction. In the presented method, an correlation matrix of array response vectors is obtained through integration over the direction range and a minimization problem is formulated using some eigenvectors of the correlation matrix such that a more accurate steering vector than initially given one can be found. The minimization problem is transformed into a relaxed SDP (semidefinite program) problem, which can be effectively solved since it is a sort of convex optimization. Simulation results show that the proposed method outperforms existing ones such as ORM (outside-range-based method) and USM (uncertainty-based method).

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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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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• v.14 no.6
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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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• v.14 no.1
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.9A
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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.