• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.647-654
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• 2017

Duality methods based on modified Lagrangian functional for solving a model crack problem is considered. Without additional assumptions of regularity of the solution of an initial problem duality ratio is established for initial and dual problem.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.2
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• pp.13-46
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• 2001

SDP (Semidefinite Programming), as a sort of “cone-LP”, optimizes a linear function over the intersection of an affine space and a cone that has the origin as its apex. SDP, however, has been developed in the process of searching for better solution methods for NP-hard combinatorial optimization problems. We surveyed the basic theories necessary to understand SDP researches. First, We examined SDP duality, comparing it to LP duality, which is essential for the interior point method, Second, we showed that SDP can be optimized from an interior solution in polynomial time with a desired error limit. finally, we summarized several research papers that showed SDP can improve solution methods for some combinatorial optimization problems, and explained why SDP has become one of the most important research topics in optimization. We tried to integrate SDP theories. relatively diverse and complicated. to survey research papers with our own perspective, and thus to help researcher to pursue their SDP researches in depth.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.179-192
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• 2012

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maximization problem is used and we get the same results as in the paper [21].

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1533-1539
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• 2011

In this paper, a class of nonlinear bilevel programs, i.e. the lower level problem is linear programs, is considered. Aiming at this special structure, we append the duality gap of the lower level problem to the upper level objective with a penalty and obtain a penalized problem. Using the penalty method, we give an existence theorem of solution and propose an algorithm. Then, a numerical example is given to illustrate the algorithm.

• East Asian mathematical journal
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• v.27 no.1
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• pp.11-21
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• 2011

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.11
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• pp.235-242
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• 2021

The paper aims to examine the relationship between the Board of Directors' characteristics and the timeliness of financial statements of listed firms in Vietnam. Accordingly, research data was collected from the FiinPro Platform database system, which included financial statements of 548 organizations listed on the Hochiminh Stock Exchange and the Hanoi Stock Exchange from 2013 to 2018. The paper employs the OLS regression method with a strong standard error method and FGLS to handle the problem of variable variance and autocorrelation. The research results show that the following three factors have significant impacts on the timeliness of financial statements: the duality of Chairman, the age of Chairman, and the change of members of the Board of Directors. The findings suggest that the duality of the Chairman of the Board of Directors will lead to a decrease in control effectiveness, adversely affecting the timeliness of the financial statements. In addition, the change of members in the Board of Directors will lead to a positive change in the timely provision of information. The age of the Chairman of the Board of Directors also positively impacts the timeliness of financial statements.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.27-46
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• 1998

We are concerned with an optimal control problem governed by a Poisson equation in which body force acts like a control parameter. The cost functional to be optimized is taken to represent the error from the desired observation and the cost due to the control. We recast the problem into the mixed formulation to take advantage of the minimax principle for the duality method. The existence of a saddle point for the Lagrangian shall be shown and the optimality system will be derived therein. Finally, to attain an optimal control, we combine the optimality system with an operational technique. By achieving the gradient of the cost functional, a convergent algorithm based on the projected gradient method is established.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1195-1207
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• 2015

Lagrange multiplier method for solving the contact problem in elasticity is considered. Based on lower semicontinuity of sensitivity functional we prove the convergence of modified dual scheme to corresponding saddle point.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.106.2-106
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• 2001

The two typical composite operations of fuzzy relation are the max-min and the min-max composite operations. It is known that the two operations can be completely dual. This paper pays attention to the nature that these two typical operations are completely dual and investigates the correlation between the max-min composite relation equation and the min-max composite relation equation. An important scheme of correlation is in the characteristic of solution sets derived from these two fuzzy relation equations. The paper explains that one of the composite fuzzy relation equations is solvable using the solution method of the other fuzzy relation equation. The above-mentioned duality plays an important role in this solution procedure. Since it is not necessary to build the solution method separately like before, calculation efficiency can be raised. Moreover, the solution for the relation ...

• Journal of Korean Society of Industrial and Systems Engineering
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• v.10 no.16
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• pp.183-195
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• 1987

The effectiveness of quality control is contingent to adaptability to the present circumstance. The objectives of this study are to provide empirical data to carry out qualify control effectively. To accomplish this purpose, an empirical study was made by questionaire (mailing survey method, Feb. to Mar. in 1987). The sample is the 167 companies in Korean manufacturing industry. The main findings out of the analysis are as follows the stage of quality control is concentrated in appraisal phase, the company standard is equiped gradually in non-KS marked company and the need of economic evaluation about quality control is increased gradually. With a view to analysing of relationship between quality control and it's effect factors (company standard, KS mark, computer based information system), the methods of $\chi$$^2$ test are used. The company standard have a significant difference in top manager's altitude to duality control, operation stage of quality control. operation scope of qualify control and quality budgeting system but is insignificant with economic evaluation about duality control. Otherwise, KS mark is insignificant with the equality control activity except for operation scope. The quality information system based in computer have a significant difference in operation stage, operation scope and economic evaluation. Therefor, for the purpose of attaining effectiveness of quality control through the economic evaluation about quality control, the company standard and computer based duality information system must be utilized in quality control activity.