• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• Management Science and Financial Engineering
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• v.17 no.2
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• pp.63-84
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• 2011

The ordinary multiple criteria decision making (MCDM) approach requires two types of input, alternative values and criterion weights, and employs two schemes of alternative prioritization, dominance and potential optimality. This paper allows for incomplete information on both types of input and gives rise to the dominance relationships and potential optimality of alternatives. Unlike the earlier studies, we emphasize that incomplete information frequently takes the form of strict inequalities, such as strict orders and strict bounds, rather than weak inequalities. Then the issues of rising importance include: (1) The standard mathematical programming approach to prioritize alternatives cannot be used directly, because the feasible region for the permissible decision parameters becomes an open set. (2) We show that the earlier methods replacing the strict inequalities with weak ones, by employing a small positive number or zeroes, which closes the feasible set, may cause a serious problem and yield unacceptable prioritization results. Therefore, we address these important issues and develop a useful and simple method, without selecting any small value for the strict preference information. Given strict information on both types of decision parameters, we first construct a nonlinear program, transform it into a linear programming equivalent, and finally solve it via a two-stage method. An application is also demonstrated herein.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.68 no.1
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• pp.27-35
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• 2019

There is a growing interest in various microgrid solutions that supply electricity 24 hours a day to off-grid areas where are not connected with the main grid, and Korea has many positive effects by constructing overseas microgrids as a country operating the emission trading scheme. Since it is not clear how to obtain load curves that is one of the inputs of the HOMER used to design a microgrid optimization plan, or it is necessary to examine whether electricity is supplied to the peak load level of the areas where have not received the electricity benefits from the viewpoint of the demand management, a methodology should be developed to know the load composition ratio and the shape of the daily load curve. In this paper, the relative coefficient and average load information for each load group obtained from the survey are used besides peak load and total average load. A mathematical model is proposed to derive the load composition ratio in the form of a Quadratic Programming and the load forecasting is performed using simple linear regression with future indicators. The effectiveness of the proposed method is confirmed for the Philippine island region supported by Korea Energy Agency and the Asian Development Bank.

• Communications of Mathematical Education
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• v.34 no.4
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• pp.563-585
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• 2020

This study developed teaching-learning materials for mathematics and coding convergence classes using Python, focusing on 'Prime Factorization' of seventh graders. After applying the teaching methods and contents to the students, they analyzed whether the learners achieved their learning goals. The results were used to modify and supplement teaching and learning materials. Affective domain of learners were also analyzed. The results are that the teaching methods and contents of the developed teaching-learning materials were generally appropriate for learners. The learners understood most of the lessons according to the set teaching methods of all classes. And learners have mostly reached their learning goals. In addition, as a result of analyzing the definition characteristics of learners through follow-up interviews, the interest in mathematics and programming has improved. The developed teaching and learning materials of this study are well consisted mostly of the teaching methods and the contents of the classes, and are organized so that learners can reach most of the learning goals. It also brought positive changes to the affective domain of mathematics and coding, demonstrating the potential for useful use in school.

• Journal of Korea Trade
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• v.24 no.1
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• pp.171-207
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• 2020

Purpose - This paper investigates the potential effect of the Regional Comprehensive Economic Partnership (RCEP) on trade liberalization among member countries in order to answer key questions in our research on whether the RCEP will be a cornerstone or just collaboration. Furthermore, it aims to measure the likely magnitude of the economic impact it has on its members. Design/methodology - Toward achieving research objectives, we developed a regional CGE model based on the GTAP 9 database. Findings - The simulation results show Korea, Australia, India, and Japan ranked the top countries with an average growth in GDP of 0.38 %, 0.36%, 0.29%, and 0.23%, respectively. Moreover, China and New Zealand followed with a percentage of 0.12% each. The lower economic performing group is the ASEAN group due to a contraction in GDP by 0.13%. Accordingly, there was a positive impact of the RCEP agreement on all member states, as empirically demonstrated. Furthermore, Korea is one of the countries that will benefit most from joining this agreement. Finally, this agreement is important; it has many economic benefits to member states, but it is not a cornerstone. Originality/value - The examination of the quantitative effects of tariff removal among the RCEP's countries is its value. We will address all member countries of the convention simultaneously using a regional CGE model GAMS language, where we employed a Mathematical Programming System for General Equilibrium (MPSGE) to establish a Regional CGE model. This study is directed to policymakers looking at evaluating RCEP agreement.