• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.149-159
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• 2009

In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.

• Steel and Composite Structures
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• v.27 no.1
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.2
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• pp.43-49
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• 2000

It is a complex process to analyze power system voltage stability problems with all of the dynamics of a system, because a large power network system sophisticatedly consists of generators, lines, loads and so forth. So we considered the dynamics of loads so as to analyze voltage stability method- by carrying out an analysis of steady state voltage stability and dynamic voltage stability simultaneously. To perform a steady state voltage stability program in advance makes it possible to cut down on laborious calculations so that an analysis of dynamic voltage stability becomes concise. The validity and efficiency of the method presented in this paper were verified by applying the IEEE 14 bus system.

• Journal of Satellite, Information and Communications
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• v.12 no.4
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• pp.100-105
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• 2017

In this paper, we study an interference avoidance scenario in the presence of a interferer which can rapidly observe the transmit power of backscatter communications and effectively interrupt backscatter signals. We consider a power control with a sub-channel allocation to avoid interference attacks and a power-splitting ratio for backscattering and RF energy harvesting in sensors. We formulate the problem based on a Stackelberg game theory and compute the optimal transmit power, power-splitting ratio, and sub-channel allocation parameter to maximize a utility function against the interferer. We propose the utility maximization using Lagrangian dual decomposition for the backscatter communications and the interferer to prove the existence of the Stackelberg equilibrium. Numerical results show that the proposed algorithms effectively maximize the utility, compared to that of the algorithm based on the Nash game, so as to overcome a malicious interference in backscatter communications.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.1
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• pp.149-168
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• 2015

In cognitive radio networks (CRNs), hybrid overlay and underlay sharing transmission mode is an effective technique for improving the efficiency of radio spectrum. Unlike existing works in the literature, where only one secondary user (SU) uses overlay and underlay modes, the different transmission modes should be allocated to different SUs, according to their different quality of services (QoS), to achieve the maximal efficiency of radio spectrum. However, hybrid sharing mode allocation for heterogeneous services is still a challenge in CRNs. In this paper, we propose a new resource allocation method for hybrid sharing transmission mode of overlay and underlay (HySOU), to achieve more potential resources for SUs to access the spectrum without interfering with the primary users. We formulate the HySOU resource allocation as a mixed-integer programming problem to optimize the total system throughput, satisfying heterogeneous QoS. To decrease the algorithm complexity, we divide the problem into two sub-problems: subchannel allocation and power allocation. Cutset is used to achieve the optimal subchannel allocation, and the optimal power allocation is obtained by Lagrangian dual function decomposition and subgradient algorithm. Simulation results show that the proposed algorithm further improves spectrum utilization with a simultaneous fairness guarantee, and the achieved HySOU diversity gain is a satisfactory improvement.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1229-1244
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• 2017

In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.