• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2014.05a
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• pp.89-93
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• 2014

Reviews are very important for potential consumer' making choices. They are also used by manufacturers to find problems of their products and to collect competitors' business information. But someone write fake reviews to mislead readers to make wrong choices. Therefore detecting fake reviews is an important problem for the E-commerce sites. Support Vector Machines (SVMs) are very important text classification algorithms with excellent performance. In this paper, we propose a new incremental algorithm based on weight and the extension of Karush-Kuhn-Tucker(KKT) conditions and Convex Hull for online Review Spam Detection. Finally, we analyze its performance in theory.

• Journal of Communications and Networks
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• v.18 no.4
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• pp.629-638
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• 2016

In this paper, we investigate an energy-efficient resource allocation problem in a two-way relay (TWR) network consisting of multiple user pairs and an amplify-and-forward (AF) relay. As the users and relay have individual energy efficiencies (EE), we formulate a multi-objective optimization problem (MOOP). A single-objective optimization problem (SOOP) of the MOOP is introduced using a weighted-sum method, which achieves a single Pareto optimal point of the MOOP. To derive the algorithm for the SOOP, we propose a more tractable equivalent problem using the Karush-Kuhn-Tucker conditions of the SOOP, which guarantees convergence at the local optimal points. The proposed equivalent problem can be efficiently solved by the proposed iterative algorithm. Numerical results demonstrate the effectiveness of the proposed algorithm in achieving the optimal EE in multi-user AF TWR networks.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.147-163
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• 2017

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.7A
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• pp.562-567
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• 2009

In this paper, two-hop beamforming relay system, with source, relay, and destination nodes, is considered and the transmit- and receive-beamforming vectors and the relay processing matrix are designed for minimizing a mean square error (MMSE) between the transmit and receive signals. Here, to reduce the transmit power of the source or the relay, two local inequality constraints are involved with MMSE problem. By adopting the Lagrange method, closed formed Karush-Kuhn-Tucker (KKT) conditions (equalities) are derived and an iterative algorithm is developed to solve the entangled KKT equalities. Due to the inequality power constraints, the source or the relay can reduce its transmit power when the received signal-to-noise ratios (SNRs) of the first- and the second-hop are different. Meanwhile, the destination can achieve almost identical bit-error-rate performance compared to an optimal beamforming system maximizing the received SNR. This claim is supported by a computer simulation.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.4
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• pp.182-188
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• 2013

In this paper, we propose a complex-valued support vector machine (SVM) classifier which process the complex valued signal measured by pulse doppler radar (PDR) to identify moving targets from the background. SVM is widely applied in the field of pattern recognition, but features which used to classify are almost real valued data. Proposed complex-valued SVM can classify the moving target using real valued data, imaginary valued data, and cross-information data. To design complex-valued SVM, we consider slack variables of real and complex axis, and use the KKT (Karush-Kuhn-Tucker) conditions for complex data. Also we apply radial basis function (RBF) as a kernel function which use a distance of complex values. To evaluate the performance of the complex-valued SVM, complex valued data from PDR were classified using real-valued SVM and complex-valued SVM. The proposed complex-valued SVM classification was improved compared to real-valued SVM for dog and human, respectively 8%, 10%, have been improved.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.1
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• pp.47-58
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• 2018

The heterogeneous cellular network (HCN) is most significant as a key technology for future fifth generation (5G) wireless networks. The heterogeneous network considered consists of randomly macrocell base stations (MBSs) overlaid with femtocell base stations (BSs). The stochastic geometry has been shown to be a very powerful tool to model, analyze, and design networks with random topologies such as wireless ad hoc, sensor networks, and multi- tier cellular networks. The HCNs can be energy-efficiently designed by deploying various BSs belonging to different networks, which has drawn significant attention to one of the technologies for future 5G wireless networks. In this paper, we propose switching off/on systems enabling the BSs in the cellular networks to efficiently consume the power by introducing active/sleep modes, which is able to reduce the interference and power consumption in the MBSs and FBSs on an individual basis as well as improve the energy efficiency of the cellular networks. We formulate the minimization of the power onsumption for the MBSs and FBSs as well as an optimization problem to maximize the energy efficiency subject to throughput outage constraints, which can be solved the Karush Kuhn Tucker (KKT) conditions according to the femto tier BS density. We also formulate and compare the coverage probability and the energy efficiency in HCNs scenarios with and without coordinated multi-point (CoMP) to avoid coverage holes.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.40 no.4
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• pp.105-111
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• 2017

Vendor Managed Inventory is a well-known vendor-retailer coordination approach in supply chain management where the vendor manages inventory of the retailer and determines the order interval and order quantity for the retailer. To consider practical situation, the upper limit of inventory for the retailer is set. If the inventory level for the retailer exceeds the upper limit, then the penalty cost is charged to the retailer. Furthermore, maximum allowable inventory level is set for the vendor to prevent the vendor from keeping much inventory. Single-vendor multi-retailer supply chain model with upper limit of inventory for vendor and retailers is studied. All the retailers' are assumed to have the common cycle time, and a vendor manages retailers' inventory and replenishes products. The mathematical formulation is introduced to minimize the total cost including the penalty cost violating the upper limit of inventory for retailers with the constraint of maximum allowable inventory level. The solution procedure based on Karush-Kuhn-Tucker (KKT) conditions is derived. KKT conditions are often applied to find an optimal solution of nonlinear programming problem with constraints. An illustrative example is used to show the application of the proposed solution procedure. Furthermore, sensitivity analysis is done to find out the relationship between maximum allowable inventory level and other values such as order quantity, the number of shipment, vendor's cost, retailer's cost, and total cost. As maximum allowable inventory level decreases, the number of shipment decreases but total cost increases. Order quantity has the trend of decline and is affected by the number of shipment.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.7
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• pp.3134-3155
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• 2020

In this paper, we study the joint radio and computational resource allocation in the ultra-dense mobile-edge computing networks. In which, the scenario which including both computation offloading and communication service is discussed. That is, some mobile users ask for computation offloading, while the others ask for communication with the minimum communication rate requirements. We formulate the problem as a joint channel assignment, power control and computational resource allocation to minimize the offloading cost of computing offloading, with the precondition that the transmission rate of communication nodes are satisfied. Since the formulated problem is a mixed-integer nonlinear programming (MINLP), which is NP-hard. By leveraging the particular mathematical structure of the problem, i.e., the computational resource allocation variable is independent with other variables in the objective function and constraints, and then the original problem is decomposed into a computational resource allocation subproblem and a joint channel assignment and power allocation subproblem. Since the former is a convex programming, the KKT (Karush-Kuhn-Tucker) conditions can be used to find the closed optimal solution. For the latter, which is still NP-hard, is further decomposed into two subproblems, i.e., the power allocation and the channel assignment, to optimize alternatively. Finally, two heuristic algorithms are proposed, i.e., the Co-channel Equal Power allocation algorithm (CEP) and the Enhanced CEP (ECEP) algorithm to obtain the suboptimal solutions. Numerical results are presented at last to verify the performance of the proposed algorithms.

• Journal of Electrical Engineering and Technology
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• v.13 no.3
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• pp.1069-1078
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• 2018

Demand response (DR) programs give opportunity to consumers to manage their electricity bills. Besides, distribution system operator (DSO) is interested in using DR programs to obtain technical and economic benefits for distribution network. Since small consumers have difficulties to individually take part in the electricity market, an entity named demand response provider (DRP) has been recently defined to aggregate the DR of small consumers. However, implementing DR programs face challenges to fairly allocate benefits and payments between DRP and DSO. This paper presents a procedure for modeling the interaction between DRP and DSO based on a bilevel programming model. Both DSO and DRP behave from their own viewpoint with different objective functions. On the one hand, DRP bids the potential of DR programs, which are load shifting and load curtailment, to maximize its expected profit and on the other hand, DSO purchases electric power from either the electricity market or DRP to supply its consumers by minimizing its overall cost. In the proposed bilevel programming approach, the upper level problem represents the DRP decisions, while the lower level problem represents the DSO behavior. The obtained bilevel programming problem (BPP) is converted into a single level optimizing problem using its Karush-Kuhn-Tucker (KKT) optimality conditions. Furthermore, point estimate method (PEM) is employed to model the uncertainties of the power demands and the electricity market prices. The efficiency of the presented model is verified through the case studies and analysis of the obtained results.