• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.513-533
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• 2004

We present the pricing and hedging method for options with general payoffs in the presence of transaction costs. The convexity of the payoff function-gamma of the options- is an important issue under transaction costs. When the payoff function is convex, Leland-style pricing and hedging method still works. However, if the payoff function is of general form, additional assumptions on the size of transaction costs or of the hedging interval are needed. We do not assume that the payoff is convex as in Leland 〔11〕 and the value of the Leland number is less (bigger) than 1 as in Hoggard et al. 〔10〕, Avellaneda and Paras 〔1〕. We focus on generally recognized asymmetry between the option sellers and buyers. We decompose an option with general payoff into difference of two options each of which has a convex payoff. This method is consistent with a scheme of separating out the seller's and buyer's position of an option. In this paper, we first present a simple linear valuation method of general payoff options, and also propose in the last section more efficient hedging scheme which costs less to hedge options.

• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.153-162
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• 2001

In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

• Proceedings of the Korean Information Science Society Conference
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• 2005.07a
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• pp.892-894
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• 2005

Graph partitioning provides an important tool for data clustering, but is an NP-hard combinatorial optimization problem. Spectral clustering where the clustering is performed by the eigen-decomposition of an affinity matrix [1,2]. This is a popular way of solving the graph partitioning problem. On the other hand, semidefinite relaxation, is an alternative way of relaxing combinatorial optimization. issuing to a convex optimization[4]. In this paper we present a semidefinite programming (SDP) approach to graph equi-partitioning for clustering and then we use eigen-decomposition to obtain an optimal partition set. Therefore, the method is referred to as semidefinite spectral clustering (SSC). Numerical experiments with several artificial and real data sets, demonstrate the useful behavior of our SSC. compared to existing spectral clustering methods.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.7
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• pp.2010-2026
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• 2024

This work investigates the hybrid precoder scheme in a millimeter wave (mmWave) multi-user MIMO system. We study a sum rate maximization scheme by jointly designing the digital precoder and the analog precoder. To handle the non-convex problem, a block coordinate descent (BCD) method is formulated, where the digital precoder is solved by a bisection search and the analog precoder is addressed by the penalty dual decomposition (PDD) alternately. Then, we extend the proposed algorithm to the sub-connected schemes. Besides, the proposed algorithm enjoys lower computational complexity when compared with other benchmarks. Simulation results verify the performance of the proposed scheme and provide some meaningful insight.

• Journal of KIISE:Software and Applications
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• v.27 no.6
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• pp.583-594
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• 2000

The thinning process which is commonly used in extracting skeletons from handwritten Hangul characters has a problem of distorting the original pattern shapes. This paper proposes a method of skeleton extraction using a shape decomposition algorithm. We decompose the character pattern into a set of near convex parts using a shape decomposition algorithm. From the shape-decomposed pattern, we detect the joint parts and extract the skeletons from the parts incident to the joint parts. Then the skeletons not incident to the joint parts are extracted. Finally, the process of skeleton extension is performed to ensure the connectivity. We setup five criteria for the comparison of quality of skeletons extracted by our method and the thinning based method. The comparison shows the superiority of our method in terms of several criteria.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.49 no.7
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• pp.23-31
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• 2012

Resource allocation, such as joint rate control and scheduling, is an important issue in cognitive radio networks. However, it is difficult to jointly consider the rate control and scheduling problem due to the stochastic behavior of channel availability in cognitive radio networks. In this paper, we propose an asymmetric joint rate control and scheduling technique under reliability constraints in cognitive radio networks. The joint rate control and scheduling problem is formulated as a convex optimization problem and substantially decomposed into several sub-problems using a dual decomposition method. An algorithm for secondary users to locally update their rate that maximizes the utility of the overall system is also proposed. The results of simulations revealed that the proposed algorithm converges to a globally optimal solution.

• Journal of KIISE:Software and Applications
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• v.29 no.1_2
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• pp.20-29
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• 2002

The composite stock cutting problem is to allocate rectangular and/or irregular patterns onto a large composite stock sheet of finite dimensions in such a way that the resulting scrap will be minimized. In this paper, the distributed simulated annealing with the new cost error tolerant spatial decomposition is applied to the composite stock cutting problem in MPI environments. The cost error tolerant scheme relaxes synchronization and chooses small perturbations on states asynchronously in a dynamically changed stream length to keep the convergence property of the sequential annealing. This paper proposes the efficient data structures for representation of patterns and their affinity relations and also shows how to determine move generations, annealing parameters, and a cost function. The spatial decomposition method is addressed in detail. This paper identifies that the final quality is not degraded with almost linear speedup. Composite stock shapes are not constrained to convex polygons or even regular shapes, but the rotations are only allowed to 2 or 4 due to its composite nature.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.11
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• pp.3008-3025
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• 2012

In this paper, the downlink resource allocation of OFDMA system with decode-and-forward (DF) relaying is investigated. A non-convex optimization problem maximizing system throughput with users' satisfaction constraints is formulated with joint relay selection, subcarrier assignment and power allocation. We first transform it to a standard convex problem and then solve it by dual decomposition. In particular, an Optimal resource allocation scheme With Time-sharing (OWT) is proposed with combination of relay selection, subcarrier allocation and power control. Due to its poor adaption to the fast-varying environment, an improved version with subcarrier Monopolization (OWM) is put forward, whose performance promotes about 20% compared with that of OWT in the fast-varying vehicular environment. In fact, OWM is the special case of OWT with binary time-sharing factor and OWT can be seen as the tight upper bound of the OWM. To the best of our knowledge, such algorithms and their relation have not been accurately investigated in cooperative OFDMA networks in the literature. Simulation results show that both the system throughput and the users' satisfaction of the proposed algorithms outperform the traditional ones.

• ETRI Journal
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• v.37 no.3
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• pp.471-479
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• 2015

Traditional designs of cognitive radio (CR) focus on maximizing system throughput. In this paper, we study the joint overlay and underlay power allocation problem for orthogonal frequency-division multiple access-based CR. Instead of maximizing system throughput, we aim to maximize system energy efficiency (EE), measured by a "bit per Joule" metric, while maintaining the minimal rate requirement of a given CR system, under the total power constraint of a secondary user and interference constraints of primary users. The formulated energy-efficient power allocation (EEPA) problem is nonconvex; to make it solvable, we first transform the original problem into a convex optimization problem via fractional programming, and then the Lagrange dual decomposition method is used to solve the equivalent convex optimization problem. Finally, an optimal EEPA allocation scheme is proposed. Numerical results show that the proposed method can achieve better EE performance.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.5
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• pp.2063-2081
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• 2018

A resource allocation algorithm is proposed in this paper to simultaneously minimize the total system power consumption and maximize the system throughput for the downlink of multi-user multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) systems. With the Lagrange dual decomposition method, we transform the original problem to its convex dual problem and prove that the duality gap between the two problems is zero, which means the optimal solution of the original problem can be obtained by solving its dual problem. Then, we use convex optimization method to solve the dual problem and utilize bisection method to obtain the optimal dual variable. The numerical results show that the proposed algorithm is superior to traditional single-objective optimization method in both the system throughput and the system energy consumption.