• 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.

• Journal of KIEE
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• v.11 no.1
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• pp.51-54
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• 2001

In this paper, a MW-Mvar investment technique focused on minimizing the system loss is presented. An optimization technique, in which the system loss is defined as the objective function and the power flow equations as the constraints, is introduced to obtain the Lagrangian multipliers λP and λQ. The Lagrangian multipliers imply the variation of the system loss with respect to incremental bus power and are used as MW-Mvar investment indices for minimizing the system loss. ΔP MW and ΔQ Mvar are invested, step by step, by the priority of λP and λQ index given for each bus. Derivation of the index uses the information from normal power flow calculation.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.469-476
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• 2012

In this paper, a finite element domain decomposition method using local and mixed Lagrange multipliers for a large scal structural analysis is presented. The proposed algorithms use local and mixed Lagrange multipliers to improve computational efficiency. In the original FETI method, classical Lagrange multiplier technique was used. In the dual-primal FETI method, the interface nodes are used at the corner nodes of each sub-domain. On the other hand, the proposed FETI-local analysis adopts localized Lagrange multipliers and the proposed FETI-mixed analysis uses both global and local Lagrange multipliers. The numerical analysis results by the proposed algorithms are compared with those obtained by dual-primal FETI method.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.613-622
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• 2023

In this paper, finite element method is applied to solve boundary control problem governed by elliptic variational inequality with an infinite number of variables. First, we introduce some important features of the finite element method, boundary control problem governed by elliptic variational inequalities with an infinite number of variables in the case of the control and observation are on the boundary is introduced. We prove the existence of the solution by using the augmented Lagrangian multipliers method. A triangular type finite element method is used.

• Korea-Australia Rheology Journal
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• v.19 no.4
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• pp.233-242
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• 2007

We performed a numerical investigation to find out the optimal choice of the spatial discretization in the distributed-Lagrangian-multiplier/fictitious-domain (DLM/FD) method for the solid/fluid interaction problem. The elastic solid bar attached on the bottom in a pressure-driven channel flow of a Newtonian fluid was selected as a model problem. Our formulation is based on the scheme of Yu (2005) for the interaction between flexible bodies and fluid. A fixed regular rectangular discretization was applied for the description of solid and fluid domain by using the fictitious domain concept. The hydrodynamic interaction between solid and fluid was treated implicitly by the distributed Lagrangian multiplier method. Considering a simplified problem of the Stokes flow and the linearized elasticity, two numerical factors were investigated to clarify their effects and to find the optimum condition: the distribution of Lagrangian multipliers and the solid/fluid interfacial condition. The robustness of this method was verified through the mesh convergence and a pseudo-time step test. We found that the fluid stress in a fictitious solid domain can be neglected and that the Lagrangian multipliers are better to be applied on the entire solid domain. These results will be used to extend our study to systems of elastic particle in the Stokes flow, and of particles in the viscoelastic fluid.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.2
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• pp.177-189
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• 2015

This paper presents an all-direct domain decomposition approach for large-scale structural analysis. The proposed approach achieves computational robustness and efficiency by enforcing the compatibility of the displacement field across the sub-domain boundaries via local Lagrange multipliers and augmented Lagrangian formulation (ALF). The proposed domain decomposition approach was compared to the existing FETI approach in terms of the computational time and memory usage. The parallel implementation of the proposed algorithm was described in detail. Finally, a preliminary validation was attempted for the proposed approach, and the numerical results of two- and three-dimensional problems were compared to those obtained through a dual-primal FETI approach. The results indicate an improvement in the performance as a result of the implementing the proposed approach.

• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.2
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• pp.47-58
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• 1988

The dynamic uncapacitated facility location model is formulated by a mixed integer programming. It has the objective of minimizing total discounted costs for meeting demands specified in different time periods at various demand centers. Costs include those for operation of facilities to demand centers and a fixed cost associated with the capital investment. The problem is decomposed into two simple Lagrangian relaxed subproblems which are coordinated by Lagrangian multipliers. We explored the effect of using the subgradient optimization procedure and a viable solution approach is proposed. Computational results are presented and further research directions are discussed.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.1003-1005
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• 1998

We present the implementation of a Lagrangian Relaxation based large scale thermal Unit Commitment problem. The problem is decomposed into thermal subproblem by using Lagrangian multipliers. The thermal subproblem is solved by using dynamic programmmg. we perform a numerical test using the thermal system of KEPCO over a week (168 hours) period. The programming language used for the test program is C. The result is compared with the priority list method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.10C
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• pp.1007-1012
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• 2003

In order to accelerate the convergence speed of the conventional BP algorithm, constrained optimization techniques are applied to the BP algorithm. First, the noise-constrained least mean square algorithm and the zero noise-constrained LMS algorithm are applied (designated the NCBP and ZNCBP algorithms, respectively). These methods involve an important assumption: the filter or the receiver in the NCBP algorithm must know the noise variance. By means of extension and generalization of these algorithms, the authors derive an adaptive error-constrained BP algorithm, in which the error variance is estimated. This is achieved by modifying the error function of the conventional BP algorithm using Lagrangian multipliers. The convergence speeds of the proposed algorithms are 20 to 30 times faster than those of the conventional BP algorithm, and are faster than or almost the same as that achieved with a conventional linear adaptive filter using an LMS algorithm.

• Structural Engineering and Mechanics
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• v.2 no.4
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• pp.313-326
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• 1994

Some structures under the action of some specific loads can be treated as consisting of rigid and deformable parts. The paper presents a way to include rigid elements into a finite element model accounting for geometrical and material nonlinearities. Lagrange multipliers technique is used to derive equations of motion for the coupled deformable-rigid system. Solution algorithm based on the elimination of the Lagrangian multipliers and dependent kinematic unknowns at the element level is described. A follow-up paper(Rojek and Kleiber 1993) complements the discussion by giving details of the computer implementation and presenting some realistic test examples.