• 한국정보통신학회논문지
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• 제4권1호
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• pp.155-163
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• 2000

최적 제어나 최적 설계에 사용되는 목적함수를 연립 방정식화하여, Newton법에 의하여 최적치를 구하는 알고리즘을 제안하였다. 제안한 방식은 도함수의 산출과 입력이 불필요한 일반 도함수를 프로그램화한 직접 미분법(DDA)에 의하여 목적함수와 초기치만을 입력하여 최적치를 구하는 간단한 방식이다. 제안한 방식을 최적 제어와 최적 설계에 적용하여 유용성을 확인하였다.

• Korean Journal of Mathematics
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• 제23권2호
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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.

• 대한수학회보
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• 제60권4호
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• pp.1101-1129
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• 2023

In this study we propose a model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature, and provide a methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function. The model and approach offer a significant advantage for computation of optimal policies for a large class of problems.

• 대한수학회보
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• 제45권3호
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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.

• 전기의세계
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• 제21권3호
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• pp.48-52
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• 1972

The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

• 한국신뢰성학회지:신뢰성응용연구
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• 제1권1호
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• pp.35-46
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• 2001

Replacement policy of a degradation system is investigated by incorporating the loss function. Loss function is defined by the deviation of the value of quality characteristic from its target value, which determines the loss cost. Cost function is comprised of the inspection cost, replacement cost and loss cost. Two cost minimization problems are formulated : 1)determination of an optimal inspection period given the state for the replacement and 2)determination of an optimal state for replacement under fixed inspection period. Simulation analysis is performed to observe the variation of total cost with respect to the variation of the parameters of loss function and inspection cost, respectively As a result, parameters of loss function are seen to be the most sensitive to the total cost. On the contrary, inspection cost is observed to be insensitive. This study can be applied to the replacement policy of a degradation system which has to produce the quality critical product.

• 한국안전학회지
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• 제30권3호
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• pp.13-19
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• 2015

Railway vehicle equipment goes back again to the state just before when failure by the repair. In repairable system, we are interested in the failure interval. As such, a statistical model of the point process, NHPP power law is often used for the reliability analysis of a repairable system. In order to derive a quantitative reliability value of repairable system, we analyze the failure data of the air brake system of the train line 7. The quantitative value is the failure intensity function that was modified, converted into a cost-rate function. Finally we studied the optimal number and optimal interval in which the costs to a minimum consumption point as cost-rate function. The minimum cost point was 194,613 (won/day) during the total life cycle of the braking system, then the optimal interval were 2,251days and the number of optimal preventive maintenance were 7 times. Additionally, we were compared to the cost of a currently fixed interval(4Y) and the optimum interval then the optimal interval is 3,853(won/day) consuming smaller. In addition, judging from the total life, "fixed interval" is smaller than 1,157 days as "optimal interval".

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.183-194
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• 2003

We will explain a new method for obtaining the nearly optimal domain for optimal shape design problems associated with the solution of a nonlinear wave equation. Taking into account the boundary and terminal conditions of the system, a new approach is applied to determine the optimal domain and its related optimal control function with respect to the integral performance criteria, by use of positive Radon measures. The approach, say shape-measure, consists of two steps; first for a fixed domain, the optimal control will be identified by the use of measures. This function and the optimal value of the objective function depend on the geometrical variables of the domain. In the second step, based on the results of the previous one and by applying some convenient optimization techniques, the optimal domain and its related optimal control function will be identified at the same time. The existence of the optimal solution is considered and a numerical example is also given.

• Journal of the Korean Data and Information Science Society
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• 제19권2호
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• pp.587-596
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• 2008

This paper develops the optimal periodic preventive maintenance policies following the expiration of warranty: renewing warranty and non-renewing warranty. After the warranty period is expired, the system undergoes the PM periodically and is minimally repaired at each failure between two successive PMs. Firstly, we determine the expected cost rate per unit time and the expected downtime per unit time for the periodic PM model. Then the overall value function suggested by Jiang and Ji(2002) is applied to obtain the optimal PM period and the optimal PM number. Finally, the numerical examples are presented for illustrative purpose.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.215-222
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• 2021

We explore an optimal consumption/portfolio and retirement problem with a CARA utility function of consumption. The relevant Bellman equation for the value function is transformed into a linear equation and the optimal strategies are obtained explicitly.