• 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.

• The Journal of the Korea institute of electronic communication sciences
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• v.16 no.4
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• pp.591-598
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• 2021

The digital phase-locked loops(DPLL) is a circuit used for phase synchronization and has been generally used in various fields such as communication and circuit fields. State estimators are used to design digital phase-locked loops, and infinite impulse response state estimators such as the well-known Kalman filter have been used. In general, the performance of the infinite impulse response state estimator-based digital phase-locked loop is excellent, but a sudden performance degradation may occur in unexpected situations such as inaccuracy of initial value, model error, and disturbance. In this paper, we propose a minimum variance finite impulse response filter with optimal horizon for designing a new digital phase-locked loop. A numerical method is introduced to obtain the measured value interval length, which is an important parameter of the proposed finite impulse response filter, and to obtain a gain, the covariance matrix of the error is set as a cost function, and a linear matrix inequality is used to minimize it. In order to verify the superiority and robustness of the proposed digital phase-locked loop, a simulation was performed for comparison and analysis with the existing method in a situation where noise information was inaccurate.