• East Asian mathematical journal
• /
• v.29 no.5
• /
• pp.491-501
• /
• 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
• /
• v.35 no.5
• /
• pp.547-557
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.17-35
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.37 no.4
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.287-305
• /
• 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
• /
• v.28 no.6
• /
• pp.47-51
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.241-258
• /
• 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
• /
• v.29 no.1_2
• /
• pp.337-349
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.2
• /
• pp.431-439
• /
• 1996

New design principles nad necessary conditions for a mechanical system have been suggested to be kept in the design process using a washing machine transmission as a model. The necessary conditions are funcitnal requirement condition and spatial arrangement condition. The design principles to satisfy the necessary conditions are the principle of sequence and the principle of expansion. Decision sequence for state variables and design varibles of various mechanicla elements have been formulated. New automatic design program for washing machine transmission has been developed observing the necessary conditions and design principles investigated in this study. It was verified to be very effective to follow the design conditions, principles nad formulated decision sequence in mechanical system design process.

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