• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.869-879
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• 2022

In this paper, we consider matrix optimization problems. We investigate augmented Lagrangian methods of multipliers and alternating direction methods of multipliers for the problems. Following the proofs of Eckstein [3], and Eckstein and Yao [5], we prove convergence theorems for augmented Lagrangian methods of multipliers and alternating direction methods of multipliers for the problems.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.7
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• pp.1078-1082
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• 2017

This paper presents an L1 optimization based filtering technique which effectively eliminates the optical misalignment effects encountered in the squint guidance mode with strapdown seekers. We formulated a series of L1 optimization problems in order to separate the bias and the gradient components from the measured data, and solved them via the alternating direction method of multipliers (ADMM) and sparse matrix decomposition techniques. The proposed technique was able to rapidly detect arbitrary discontinuities and gradient changes from the measured signals, and was shown to effectively cancel the undesirable effects coming from the seeker misalignment angles. The technique was implemented on embedded flight computers and the real-time operational performance was verified via the hardware-in-the-loop simulation (HILS) tests in parallel with the automatic target recognition algorithms and the intra-red synthetic target images.

• Journal of the Korean Statistical Society
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• v.34 no.1
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• pp.39-47
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• 2005

We adopt the P/sub λ, T//sup M/ policy of dam to introduce a service policy with alternating service rates for a Poisson arrival queue, in which the service rate alternates depending on the number of customers in the system. The stationary distribution of the number of customers in the system is derived and, after operating costs being assigned to the system, the optimization of the policy is studied.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.395-408
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• 2024

There have been numerous studies on the characteristics of the solutions of ordinary differential equations for optimization methods, including gradient descent methods and alternating direction methods of multipliers. To investigate computer simulation of ODE solutions, we need to trace pseudo-orbits by real orbits and it is called shadowing property in dynamics. In this paper, we demonstrate that the flow induced by the alternating direction methods of multipliers (ADMM) for a C² strongly convex objective function has the eventual shadowing property. For the converse, we partially answer that convexity with the eventual shadowing property guarantees a unique minimizer. In contrast, we show that the flow generated by a second-order ODE, which is related to the accelerated version of ADMM, does not have the eventual shadowing property.

• Journal of the Korean Physical Society
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• v.73 no.10
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• pp.1577-1583
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• 2018

Tumor-treating fields therapy involves placing pads onto the patient's skin to create a low- intensity (1 - 3 V/cm), intermediate frequency (100 - 300 kHz), alternating electric field to treat cancerous tumors. This new treatment modality has been approved by the Food and Drug Administration in the USA to treat patients with both newly diagnosed and recurrent glioblastoma. To deliver the prescribed electric field intensity to the tumor while minimizing exposure of organs at risk, we developed an optimization method for the electric field distribution in the body and compared the electric field distribution in the body before and after application of this optimization algorithm. To determine the electric field distribution in the body before optimization, we applied the same electric potential to all pairs of electric pads located on opposite sides of models. We subsequently adjusted the intensity of the electric field to each pair of pads to optimize the electric field distribution in the body, resulting in the prescribed electric field intensity to the tumor while minimizing electric fields at organs at risk. A comparison of the electric field distribution within the body before and after optimization showed that application of the optimization algorithm delivered a therapeutically effective electric field to the tumor while minimizing the average and the maximum field strength applied to organs at risk. Use of this optimization algorithm when planning tumor-treating fields therapy should maintain or increase the intensity of the electric field applied to the tumor while minimizing the intensity of the electric field applied to organs at risk. This would enhance the effectiveness of tumor-treating fields therapy while reducing dangerous side effects.

• Journal of Electrical Engineering and Technology
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• v.13 no.6
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• pp.2145-2157
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• 2018

Congestion Management (CM) is an attractive research area in the electrical power transmission with the power compensation abilities. Reconfiguration and the Flexible Alternating Current Transmission Systems (FACTS) devices utilization relieve the congestion in transmission lines. The lack of optimal power (real and reactive) usage with the better transfer capability and minimum cost is still challenging issue in the CM. The prediction of suitable place for the energy resources to control the power flow is the major requirement for power handling scenario. This paper proposes the novel optimization principle to select the best location for the energy resources to achieve the real-reactive power compensation. The parameters estimation and the selection of values with the best fitness through the Symmetrical Distance Travelling Optimization (SDTO) algorithm establishes the proper controlling of optimal power flow in the transmission lines. The modified fitness function formulation based on the bus parameters, index estimation correspond to the optimal reactive power usage enhances the power transfer capability with the minimum cost. The comparative analysis between the proposed method with the existing power management techniques regarding the parameters of power loss, cost value, load power and energy loss confirms the effectiveness of proposed work in the distributed renewable energy systems.

• Steel and Composite Structures
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• v.27 no.1
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• pp.27-33
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• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.6
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• pp.413-421
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• 2015

Regularized Blind Deconvolution is a problem applicable in degraded images in order to bring the original image out of blur. Multichannel blind Deconvolution considered as an optimization problem. Each step in the optimization is considered as variable splitting problem using an algorithm called Alternating Minimization Algorithm. Each Step in the Variable splitting undergoes Augmented Lagrangian method (ALM) / Bregman Iterative method. Regularization is used where an ill posed problem converted into a well posed problem. Two well known regularizers are Tikhonov class and Total Variation (TV) / L2 model. TV can be isotropic and anisotropic, where isotropic for L2 norm and anisotropic for L1 norm. Based on many probabilistic model and Fourier Transforms Image deblurring can be solved. Here in this paper to improve the performance, we have used an adaptive regularization filtering and isotropic TV model Lp norm. Image deblurring is applicable in the areas such as medical image sensing, astrophotography, traffic signal monitoring, remote sensors, case investigation and even images that are taken using a digital camera / mobile cameras.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.686-689
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• 2008

The leaning angle optimization of turbine blade using the genetic algorithm was conducted in this paper. The calculation CFD technique was based upon the Diagonalized Alternating Directional Implicit scheme(DADI) with algebraic turbulence modeling. The leaning angle of VKI turbine blade was represented using B-spline curve. The control points are the design variable. Genetic algorithm was taken into account as an optimization tool. The objective was to minimize the total pressure loss. The optimized final geometry shows the better aerodynamic performance compared with the initial turbine blade.

• Steel and Composite Structures
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• v.48 no.5
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• pp.583-597
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• 2023

This paper introduces a novel approach to multi-material topology optimization (MTO) targeting in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates, employing an alternative active phase approach. The mathematical formulation integrates a first shear deformation theory (FSDT) to address compliance minimization as the objective function. Through an alternating active-phase algorithm in conjunction with the block Gauss-Seidel method, the study transforms a multi-phase topology optimization challenge with multi-volume fraction constraints into multiple binary phase sub-problems, each with a single volume fraction constraint. The investigation focuses on IBFG materials that incorporate adequate local bulk and shear moduli to enhance the precision of material interactions. Furthermore, the well-established mixed interpolation of tensorial components 4-node elements (MITC4) is harnessed to tackle shear-locking issues inherent in thin plate models. The study meticulously presents detailed mathematical formulations for IBFG plates in the MTO framework, underscored by numerous numerical examples demonstrating the method's efficiency and reliability.