• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.273-286
• /
• 2005

Parameter identification problem of a three species (predator, mutualist-prey, and mutualist) ecological system with reaction-diffusion phenomenon is investigated in this paper. The mathematical model of the parameter identification problem is constructed and continuous dependence of the solution for the direct problem on the parameters identified is obtained. Finally, the existence of optimal solution and an optimality necessary condition for the parameter identification problem are given.

• 대한수학회지
• /
• 제37권4호
• /
• pp.625-643
• /
• 2000

In this paper we formulate an optimal control problem governed by time-delay Volterra integral equations; the problem includes control constraints as well as terminal equality and inequality constraints on the terminal state variables. First, using a special type of state and control variations, we represent a relatively simple and self-contained method for deriving new necessary conditions in the form of Pontryagin minimum principle. We show that these results immediately yield classical Pontryagin necessary conditions for control processes governed by ordinary differential equations (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.

• 대한수학회논문집
• /
• 제25권1호
• /
• pp.139-147
• /
• 2010

A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

• 한국신뢰성학회지:신뢰성응용연구
• /
• 제17권2호
• /
• pp.129-135
• /
• 2017

Purpose: This article provides step-stress accelerated degradation test (ADT) plans based on the Wiener process. Method: Step-stress levels and the stress change times are determined based on the D-optimality criteria to develop test plans. Further, a simple grid search method is provided for obtaining the optimal test plan. Results: Based on the solution procedure, ADT plans which include the stress levels and change times are developed for conducting the reliability test. Conclusion: Optimal step-stress ADT plans are provided for the case where the number of measurements is small.

• 자원ㆍ환경경제연구
• /
• 제15권4호
• /
• pp.673-692
• /
• 2006

고갈자원 사용의 동태적 효율성 여부를 검증하기 위해서는 미채굴된 자원의 암묵가격을 추정해야 하는데 기존 연구에서는 자원산업의 한계수입과 한계비용의 차이로 측정하거나 자원채굴량을 준고정시킨 제약비용함수를 추정하여 자원채굴량으로 편미분함으로써 도출하는 방식을 사용하였다. 그러나 이들 방법들은 채굴 투입요소인 자본의 비가단성으로 인하여 일관성이 결여된 추정치가 도출될 개연성, 시장의 독점력에 따라 변하는 한계수입의 가변성 문제와, 불완전한 재화 및 요소시장, 정부규제 등이 존재하는 현실적 상황에서 제약비용함수를 이용할 경우 전제 조건인 생산비용의 최소화가 달성되지 못함으로써 야기될 수 있는 분석결과의 신뢰성 문제 등을 안고 있다. 기존 선행연구의 방법론적 한계점들을 인식하여 본 연구에서는 좀더 일반적이고 현실적 상황에서 고갈자원 사용의 동태적 효율성 여부를 검증할 수 있는 방법을 제시한다. Shephard (1970)의 투입물거리함수를 실증적 모형의 이론적 틀로 활용함으로써 생산요소의 투입량과 최종재화의 산출량에 대한 정보만으로 추정이 가능하고, 생산비용 최소화의 극히 제한적인 상황을 전제하지 않으며, 특히 선형계획기법을 적용함으로써 시계열자료나 합동자료로 회귀 추정할 경우 발생할 수 있는 오차항의 자기상관 문제에 초연할 수 있다. 2%, 5%, 10%, 15%, 20%의 고정 할인율 폭과 실질 이자율의 25%, 50%,100%, 200%, 400%로 산정한 변동할인율을 각각 적용하여 1970년~1993닐 기간 동안 국내 무연탄 채굴의 동태적 효율성 여부를 조사한 결과 고정할인율과 변동할인율 모두에 대해서 국내 무연탄의 세대간 효율적 사용은 이루어지지 않은 것으로 나타났다.

• Journal of applied mathematics & informatics
• /
• 제27권1_2호
• /
• pp.365-374
• /
• 2009

Under certain conditions, we use augmented Lagrangians to transform a class of generalized semi-infinite min-max problems into common semi-infinite min-max problems, with the same set of local and global solutions. We give two conditions for the transformation. One is a necessary and sufficient condition, the other is a sufficient condition which can be verified easily in practice. From the transformation, we obtain a new first-order optimality condition for this class of generalized semi-infinite min-max problems.

• Communications for Statistical Applications and Methods
• /
• 제15권2호
• /
• pp.213-228
• /
• 2008

Using a linear loss function, this paper considers the one-sided testing problem for the exponential distribution via the empirical Bayes(EB) approach. Based on right censored data, we propose an EB test for the exponential parameter and obtain its convergence rate and asymptotic optimality, firstly, under the condition that the censoring distribution is known and secondly, that it is unknown.

• 대한수학회지
• /
• 제36권1호
• /
• pp.173-192
• /
• 1999

We study a boundary optimal control problem of the fluid flow governed by the Navier-Stokes equations. the control problem is formulated with the flow through a channel with steps. The first-order optimality condition of the optimal control is derived. Finite element approximations of the solutions of the optimality system are defined and optimal error estimates are derived. finally, we present some numerical results.

• 한국정밀공학회지
• /
• 제19권11호
• /
• pp.137-145
• /
• 2002

Electric vehicle body has to be subjected to uniform load and requires auxiliary equipment such as air pipe and electric wire pipe. Especially, the cross beam supports the weight of passenger and electrical equipments. a lightweight vehicle body is salutary to save operating costs and fuel consumption. Therefore this study is to perform the size and the shape optimization of crossbeam for electric vehicle using the method of topology optimization to introduce the concept of homogenization based on optimality criteria method which is efficient for the problem having the number of design variables and a few boundary condition. this provides the method to determine the optimum position and shape of circular hole in the cross beam and then can achieve the optimal design to reduce weight.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2004년도 ICCAS
• /
• pp.460-465
• /
• 2004

In this paper, we present some properties on receding horizon $H_{\infty}$ control for nonlinear discrete-time systems. First, we propose the nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems. Under this condition, noninceasing monotonicity of the saddle point value of the finite horizon dynamic game is shown to be guaranteed. We show that the derived condition on the terminal cost ensures the closed-loop internal stability. The proposed receding horizon $H_{\infty}$ control guarantees the infinite horizon $H_{\infty}$ norm bound of the closed-loop systems. Also, using this cost monotonicity condition, we can guarantee the asymptotic infinite horizon optimality of the receding horizon value function. With the additional condition, the global result and the input-to-state stable property of the receding horizon value function are also given. Finally, we derive the stability margin for the saddle point value based receding horizon controller. The proposed result has a larger stability region than the existing inverse optimality based results.