• East Asian mathematical journal
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• 제29권5호
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• pp.491-501
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• 2013

This paper is concerned with the necessary conditions of the optimal boundary control for some chemotaxis equations. We obtain the existence and the necessary conditions of the optimal boundary control in the space $(H^1(0,T))^2$. Moreover, under some assumptions, we show the uniqueness of the optimal control.

• East Asian mathematical journal
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• 제35권5호
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• pp.547-557
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• 2019

This paper is concerned with the necessary conditions for optimal control problem governed by some ODE-PDE systems. That is, we obtain the necessary conditions for optimal control by showing the differentiability of the solution with respect to the control.

• 대한수학회지
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• 제42권1호
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• pp.17-35
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• 2005

Necessary conditions for a deterministic optimal control problem which involves states constraints are derived in the form of a maximum principle. The conditions are similar to those of F.H. Clarke, R.B. Vinter and G. Pappas who assume that the problem's data are Lipschitz. On the other hand, our data are not continuously differentiable but only differentiable. Fermat's rule and Rockafellar's duality theory of convex analysis are the basic techniques in this paper.

• 대한수학회지
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• 제37권4호
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• pp.625-643
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• 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.

• 대한수학회지
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• 제40권2호
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• 전기의세계
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• 제28권6호
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• pp.47-51
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• 1979

An optimal problem in which the dynamics is nonlinear and the cost functional includes a discontinuous integrand is investigated. By using Neustadt's abstract maximum principle, a necessary conditions in the form of Pontryagin's maximum principle is derived and it is further shown that this necessary condition is also a sufficient condition for normal problems with linear-in-the-state systems.

• 대한수학회지
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• 제43권2호
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• pp.241-258
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• 2006

This paper gives conditions under which necessary optimality conditions in a locally Lipschitz program can be expressed as the invexity of the active constraint functions or the type I invexity of the objective function and the constraint functions on the feasible set of the program. The results are nonsmooth extensions of those of Hanson and Mond obtained earlier in differentiable case.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.337-349
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• 2011

This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tucker conditions for a crisp linear programming problem.

• 대한기계학회논문집A
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• 제20권2호
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• pp.431-439
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• 1996

본 연구에서 탐구된 새로운 설계조건과 설계원칙들을 적용함으로써 세탁기용 트랜스미션으로 대표되는 기계 시스템을 효과적으로 설계할 수 있었다. 개발된 자동설계 프로그램을 이용함으로써 다양한 설계시뮬레이션을 단기간에 수행할 수 있었으며 설계 실무자로 하여금 설계변수와 상태변수 등에 관한 민감도를 파악하게 하는데 매우 효과적이었다. 본 연구에서 새롭게 제안된 시스템 설계조건들과 설계원치기들은 세탁기용 트랜스미션 뿐만 아닌 일반적인 기계시스템 설계시에도 적용될 수 있는 것으로 판단된다.

• 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.