• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1249-1262
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• 2010

An approximate alternating linearization decomposition method, for minimizing the sum of two convex functions with some separable structures, is presented in this paper. It can be viewed as an extension of the method with exact solutions proposed by Kiwiel, Rosa and Ruszczynski(1999). In this paper we use inexact optimal solutions instead of the exact ones that are not easily computed to construct the linear models and get the inexact solutions of both subproblems, and also we prove that the inexact optimal solution tends to proximal point, i.e., the inexact optimal solution tends to optimal solution.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.38 no.6
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• pp.38-45
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• 2001

In this paper, numerical stability analysis methodology for the singleton-type linguistic fuzzy control systems is proposed. The proposed stability analysis is not the analytical method but the numerical method using the convex optimization of Quadratic Programming (QP) and Linear Matrix Inequalities (LMI). Finally, the applicability of the suggested methodology is highlighted via simulation results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.6A
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• pp.855-861
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• 2000

This paper concerns a development of LQ-servo PI controller design on the basis of time-domain approach. The motivation is because the previous design techniques developed on the frequency-domain is not well suited meet the time-domain design specifications. Our development techniques used in this paper is base on the convex optimization methods including Lagrange multiplier, dual concept, semidefinite programming.

• 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 Society of Manufacturing Technology Engineers
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• v.9 no.2
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• pp.59-65
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• 2000

In this paper the comparison of the first order approximation schemes such as SLP(sequential linear programming) CONLIN(convex linearization) MMA(method of moving asymptotes) and the second order approximation scheme SQP(sequential quadratic programming) was accomplished for optimization of nonlinear structures. It was found that MMA and SQP are the most efficient methods for optimization. But the number of function call of SQP is much more than that of MMA. Therefore when it is considered with the expense of computation MMA is more efficient than SQP. In order to examine the efficiency of MMA for complex optimization problem it was applied to the helicopter tail boom con-sidering column buckling and local wall buckling constraints. it is concluded that MMA can be a very efficient approxima-tion scheme from simple problems to complex problems.

• Journal of Korean Institute of Industrial Engineers
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• v.4 no.2
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• pp.91-96
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• 1978

A modeling framework and its computational methodology for an industrial sector of the economy are investigated. The suggested industrial sector model is characterized by a programming (process analysis) representation of a production sector and an econometric estimation of the price sensitive (own and cross-prices) demands. By introducing the price sensitive demands into the process analysis representation of the production sector, it becomes possible to analyze and plan the pricing policy, the optimal production schedules and capacity expansion plans within a single framework. The computational scheme suggested in the report is based on the iterative approach each of which solves a separable convex programming problem.

• Structural Engineering and Mechanics
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• v.24 no.2
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• pp.155-180
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• 2006

Many applications in mechanical design involve elastic bodies coming into contact under the action of the applied load. The distribution of the contact pressure throughout the contact interface plays an important role in the performance of the contact system. In many applications, it is desirable to minimize the maximum contact pressure or to have an approximately uniform contact pressure distribution. Such requirements can be attained through a proper design of the initial surfaces of the contacting bodies. This problem involves a combination of two disciplines, contact mechanics and shape optimization. Therefore, the objective of the present paper is to develop an integrated procedure capable of evaluating the optimal shape of contacting bodies. The adaptive incremental convex programming method is adopted to solve the contact problem, while the augmented Lagrange multiplier method is used to control the shape optimization procedure. Further, to accommodate the manufacturing requirements, surface parameterization is considered. The proposed procedure is applied to a couple of problems, with different geometry and boundary conditions, to demonstrate the efficiency and versatility of the proposed procedure.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.3
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• pp.196-201
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• 2008

Statistical learning theory has three analytical tools which are support vector machine, support vector regression, and support vector clustering for classification, regression, and clustering respectively. In general, their performances are good because they are constructed by convex optimization. But, there are some problems in the methods. One of the problems is the subjective determination of the parameters for kernel function and regularization by the arts of researchers. Also, the results of the learning machines are depended on the selected parameters. In this paper, we propose an efficient method for objective determination of the parameters of support vector clustering which is the clustering method of statistical learning theory. Using evolutionary algorithm and bootstrap method, we select the parameters of kernel function and regularization constant objectively. To verify improved performances of proposed research, we compare our method with established learning algorithms using the data sets form ucr machine learning repository and synthetic data.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.251-261
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• 2008

In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.1
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• pp.24-30
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• 1988

We study the optimal allocation of machines and pallets in a class of manufacturing systems. The FMS is modeled as a closed queueing network with balanced loading of the stations. An Algorithm is developed, which exploits the properties of the throughput function and solves the allocation problem for increasing concave profit and convex cost. We also study the more general case of allocating machines and pallets among a set of FMSs. A dynamic programming approach is developed, which solves the problem with O(M$^{3}$N$^{2}$) operations.