• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.359-375
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• 2014

In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.1
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• pp.44-51
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• 2002

In order to generate hull form, fairness criteria applies to object function, B-spline curve vertices are considered as design variables, optimization is proceeded with satisfying geometric constraint conditions. GA(Genetic Algorithm) and optimality criteria apply to optimization process in this study.

• Journal of the Society of Naval Architects of Korea
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• v.39 no.4
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• pp.60-65
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• 2002

In order to generate hull form, we introduced optimization process. Fairness criteria is applied to object function, B-Spline control vertices are considered as design variables, optimization is proceeded with satisfying geometric constraint conditions. GA(Genetic Algorithm) and optimality criteria are applied to optimization process in this study.

• The Korean Journal of Applied Statistics
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• v.34 no.2
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• pp.279-293
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• 2021

In this paper, we introduce how to construct sufficient conditions for the oracle property in penalized linear regression model. We give formal definitions of the oracle estimator, penalized estimator, oracle penalized estimator, and the oracle property of the oracle estimator. Based on the definitions, we present a unified way of constructing optimality conditions for the oracle property and sufficient conditions for the optimality conditions that covers most of the existing penalties. In addition, we present an illustrative example and results from the numerical study.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.83-99
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• 2002

Optimality conditions are derived for a nonlinear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various duality results are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semi- definite quadratic form or an Lp norm. It is pointed out that these special cases can easily be generated from our results.

• English Language & Literature Teaching
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• v.18 no.3
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• pp.121-134
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• 2012

The purpose of this study is to investigate the optimal conditions for designing tasks appropriate to the elementary classroom based on the correspondence with the national curriculum, integration among four skills (listening, speaking, reading, and writing), authenticity, and interactivity. For this study, two primary English teachers volunteered to participate in the case study conducted in the spring semester of the 2012 school year. Each class observed was composed of 29 and 30 sixth graders (12-year-old learners). Data were collected through classroom observation and lesson plans. Optimality theory was used to analyze data from the lessons. From the findings, the overall ranking of constraints is Curriculum ${\gg}$ Integration ${\gg}$ Authenticity ${\gg}$ Interactivity. It is also shown that for teacher 'L', the tasks such as 'guessing game', 'photo of me', and 'role play' were appropriate to help students ask questions and give reasons for their choices. As for teacher 'C', the tasks such as 'hand spans', 'transport survey', and 'picture telling' needed to be considered in order to help students understand and write comparative sentences.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.283-291
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• 2015

In the optimal control problem, at first we search the expected optimal solution by using Pontryagin type's necessary conditions called the maximum principle. Next we use the sufficient conditions to conclude that the searched solution is optimal. In this article the sufficient conditions are studied. The value function is used for sufficient conditions.

• The Korean Journal of Financial Management
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• v.2 no.1
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• pp.55-75
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• 1986

This article is to analyse the economic efficiency of capital market, which plays a role of resource allocation in terms of financial claims such as stock and bond. It provides various contributions to the welfare theoretical aspects of modern capital market theory. The key feature that distinguishes the theory described here from traditional welfare theory is the presence of uncertainty. Securities has time dimensions and the state and outcome of the future are really uncertain. This problem resulting from this uncertainty can be solved by complete market, but it has a weak power to explain real stock market. Capital Market is faced with the uncertainity because it is a kind of incomplete market. Individuals and firms in capital market made their consumption-investment decision by their own criteria, i. e. the maximization of expected utility form intertemporal consumption and the maximization of the market value of firm. We noted that allocative decisions that had to be made in the economy could be naturally subdivided into two groups. One set of decisions concerned the allocation of first-period resources among consumption $C_i$, investment in risky firms $I_j$, and riskless investment M. The other decisions concern the distribution among individuals of income available in the second period $Y_i(\theta)$. Corresponing to this grouping, the theoretical analysis of efficiency has also been dichotomized. The optimality of the distribution of output in the second period is distributive efficiency" and the optimality of the allocation of first-period resources is 'the efficiency of investment'. We have found in the distributive efficiency that the conditions for attainability is the same as the conditions for market optimality. The necessary and sufficient conditions for attainability or market optimality is that (1) all utility functions are such that -$\frac{{U_i}^'(Y_i)}{{U_i}^"(Y_i)}={\mu}_i+{\lambda}Y_i$-linear risk tolerance function where the coefficients ${\mu}_i$ and $\lambda$ are independent of $Y_i$, and (2) there are homogeneous expectations, i. e. ${\Large f}_i(\theta)={\Large f}(\theta)$ for every i. On the other hand, the efficiency of investment has disagreement about optimal investment level. The investment level for market rule will not generally lead to Pareto-optimal allocation of investment. This suboptimality is caused by (1)the difference of Diamond's decomposable production function and mean-variance valuation model and (2) the selection of exelusive investment or competitive investment. In conclusion, this article has made an analysis of conditions and processes of Pareto-optimal allocation of resources in capital marker and tried to connect with significant issues in modern finance.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.4
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• pp.367-371
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• 2009

Analysis on optimality of the proportional navigation guidance(PNG) law is presented in this paper. While most of previous studies on optimality of PNG were relied on the linear formulation, this paper is based on the nonlinear formulation. The analysis shows that PNG is an optimal solution minimizing a range-weighted control energy, where the weighting function is an inverse of $\alpha$ power of the distance-to-target. We show that the navigation constant N is related to $\alpha$ directly. And also the conditions required to ensure the analysis result are investigated.