• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.11
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• pp.4087-4102
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• 2014

Two-way relaying is an effective way of improving system spectral efficiency by making use of physical layer network coding. However, energy efficiency in OFDM-based bidirectional relaying with asymmetric traffic requirement has not been investigated. In this study, we focused on subcarrier transmission mode selection, bit loading, and power allocation in a multicarrier single amplified-and-forward relay system. In this scheme, each subcarrier can operate in two transmission modes: one-way relaying and two-way relaying. The problem is formulated as a mixed integer programming problem. We adopt a structural approximation optimization method that first decouples the original problem into two suboptimal problems with fixed subcarrier subsets and then finds the optimal subcarrier assignment subsets. Although the suboptimal problems are nonconvex, the results obtained for a single-tone system are used to transform them to convex problems. To find the optimal subcarrier assignment subsets, an iterative algorithm based on subcarrier ranking and matching is developed. Simulation results show that the proposed method can improve system performance compared with conventional methods. Some interesting insights are also obtained via simulation.

• Journal of Communications and Networks
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• v.18 no.2
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• pp.173-181
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• 2016

In this paper, we address a new robust optimization problem in a multiuser multiple-input single-output broadcasting system with simultaneous wireless information and power transmission, where a multi-antenna base station (BS) sends energy and information simultaneously to multiple users equipped with a single antenna. Assuming that perfect channel-state information (CSI) for all channels is not available at the BS, the uncertainty of the CSI is modeled by an Euclidean ball-shaped uncertainty set. To optimally design transmit beamforming weights and receive power splitting, an average total transmit power minimization problem is investigated subject to the individual harvested power constraint and the received signal-to-interference-plus-noise ratio constraint at each user. Due to the channel uncertainty, the original problem becomes a homogeneous quadratically constrained quadratic problem, which is NP-hard. The original design problem is reformulated to a relaxed semidefinite program, and then two different approaches based on convex programming are proposed, which can be solved efficiently by the interior point algorithm. Numerical results are provided to validate the robustness of the proposed algorithms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.83-94
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• 2003

Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements $x^*,\;y^*{\in}H$ such that $g(x^*),\;g(y^*){\in}K$ and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T: $H\;{\rightarrow}\;H$ is a relaxed $g-{\gamma}-r-cocoercive$ and $g-{\mu}-Lipschitz$ continuous nonlinear mapping on H and g: $H{\rightarrow}\;H$ is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.10
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• pp.3887-3907
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• 2015

This paper introduces a full duplex single secondary user multiple-input multiple-output (FD-SSU-MIMO) cognitive radio network, where secondary user (SU) opportunistically accesses the authorized spectrum unoccupied by primary user (PU) and transmits data based on FD-MIMO mode. Then we study the network achievable average sum-rate maximization problem under sum transmit power budget constraint at SU communication nodes. In order to solve the trade-off problem between SU's sensing time and data transmission time based on opportunistic spectrum access (OSA) and the power allocation problem based on FD-MIMO transmit mode, we propose a simple trisection algorithm to obtain the optimal sensing time and apply an alternating optimization (AO) algorithm to tackle the FD-MIMO based network achievable sum-rate maximization problem. Simulation results show that our proposed sensing time optimization and AO-based optimal power allocation strategies obtain a higher achievable average sum-rate than sequential convex approximations for matrix-variable programming (SCAMP)-based power allocation for the FD transmission mode, as well as equal power allocation for the half duplex (HD) transmission mode.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.6
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• pp.2282-2303
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• 2021

To solve the problems of heavy computing load and system transmission pressure in energy internet (EI), we establish a three-tier cloud-edge integrated EI network based on a cloud-edge collaborative computing to achieve the tradeoff between energy consumption and the system delay. A joint optimization problem for resource allocation and task offloading in the threetier cloud-edge integrated EI network is formulated to minimize the total system cost under the constraints of the task scheduling binary variables of each sensor node, the maximum uplink transmit power of each sensor node, the limited computation capability of the sensor node and the maximum computation resource of each edge server, which is a Mixed Integer Non-linear Programming (MINLP) problem. To solve the problem, we propose a joint task offloading and resource allocation algorithm (JTOARA), which is decomposed into three subproblems including the uplink transmission power allocation sub-problem, the computation resource allocation sub-problem, and the offloading scheme selection subproblem. Then, the power allocation of each sensor node is achieved by bisection search algorithm, which has a fast convergence. While the computation resource allocation is derived by line optimization method and convex optimization theory. Finally, to achieve the optimal task offloading, we propose a cloud-edge collaborative computation offloading schemes based on game theory and prove the existence of Nash Equilibrium. The simulation results demonstrate that our proposed algorithm can improve output performance as comparing with the conventional algorithms, and its performance is close to the that of the enumerative algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.6
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• pp.2204-2224
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• 2021

This paper studies secure wireless transmission from a multi-antenna transmitter to a single-antenna intended receiver overheard by multiple eavesdroppers with considering the imperfect channel state information (CSI) of wiretap channel. To enhance security of communication link, the artificial noise (AN) is generated at transmitter. We first design the robust joint optimal beamforming of secret signal and AN to minimize transmit power with constraints of security quality of service (QoS), i.e., minimum allowable signal-to-interference-and-noise ratio (SINR) at receiver and maximum tolerable SINR at eavesdroppers. The formulated design problem is shown to be nonconvex and we transfer it into linear matrix inequalities (LMIs). The semidefinite relaxation (SDR) technique is used and the approximated method is proved to solve the original problem exactly. To verify the robustness and tightness of proposed beamforming, we also provide a method to calculate the worst-case SINR at eavesdroppers for a designed transmit scheme using semidefinite programming (SDP). Additionally, the secrecy rate maximization is explored for fixed total transmit power. To tackle the nonconvexity of original formulation, we develop an iterative approach employing sequential parametric convex approximation (SPCA). The simulation results illustrate that the proposed robust transmit schemes can effectively improve the transmit performance.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.85-102
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• 2010

Linear programming(LP) is useful for finding the best way in a given condition for some list of requirements represented as linear equations. This study analysed LP in mathematics contexts and LP in school mathematics contexts, considered learning process of LP from an epistemological point of view, and explored a hypothetical learning trajectory of LP. The differences between mathematics contexts and school mathematics contexts are whether they considered that the convex polytope $\Omega$ is feasible/infeasible or bounded/unbounded or not, and whether they prove the theorem that the optimum is always attained at a vertex of the polyhedronor not. And there is a possibility that students could not understand what is maximum and minimum of a linear function when the domain of the function is limited. By considering these three aspects, we constructed hypothetical learning trajectory consisted of 4 steps. The first step is to see a given linear expression as linear function, the second step is to partition a given domain by straight lines, the third step is to construct the conception of y-intercept by relating lines and the range of k, and the forth step is to identify whether there exists the optimum in a given domain or not.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.229-250
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• 2022

Since the publication of Markowitz's (1952) mean-variance portfolio model, research on portfolio optimization has been conducted in many fields. The existing mean-variance portfolio model forms a nonlinear convex problem. Applying Dantzig's linear programming method, it was converted to a linear form, which can effectively reduce the algorithm computation time. In this paper, we proposed a Dantzig perturbation portfolio model that can reduce management costs and transaction costs by constructing a portfolio with stable and small (sparse) assets. The average return and risk were adjusted according to the purpose by applying a perturbation method in which a certain part is invested in the existing benchmark and the rest is invested in the assets proposed as a portfolio optimization model. For a covariance estimation, we proposed a Gaussian kernel weight covariance that considers time-dependent weights by reflecting time-series data characteristics. The performance of the proposed model was evaluated by comparing it with the benchmark portfolio with 5 real data sets. Empirical results show that the proposed portfolios provide higher expected returns or lower risks than the benchmark. Further, sparse and stable asset selection was obtained in the proposed portfolios.

• Journal of the Korea Society of Computer and Information
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• v.17 no.3
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• pp.67-76
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• 2012

Traffic classification plays an important role in traffic management. To traditional methods, P2P and encryption traffic may become a problem. Support Vector Machine (SVM) is a useful classification tool which is able to overcome the traditional bottleneck. The main disadvantage of SVM algorithms is that it's time-consuming to train large data set because of the quadratic programming (QP) problem. However, the useful support vectors are only a small part of the whole data. If we can discard the useless vectors before training, we are able to save time and keep accuracy. In this article, we discussed the feasibility to remove the useless vectors through a sequential method to accelerate training speed when dealing with large scale data.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.401-404
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• 2003

In this paper, $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FIR filters are newly proposed for discrete-time state space signal models. The proposed filters require linearity, unbiased property, FIR structure, and independence of the initial state information in addition to the performance criteria in both $H_2$ and $H_{\infty}$ sense. It is shown that $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FIR filter design problems can be converted into convex programming problems via linear matrix inequalities (LMIs) with a linear equality constraint. Simulation studies illustrat that the proposed FIR filter is more robust against uncertainties and has faster convergence than the conventional IIR filters. the conventional IIR filters.