• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.757-769
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• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.435-459
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• 2004

Identification problems for the system governed by abstract nonlinear damped second order evolution equations are studied. Since unknown parameters are included in the diffusion operator, we can not simply identify them by using the usual optimal control theories. In this paper we present how to solve our identification problems via the method of transposition.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.53-68
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• 1999

To improve the slow convergence property of the steepest ascent type algorithm for continuous D-optimal design problems. we develop a new algorithm. We apply the nonlinear system of equations as the necessary condition of optimality and develop the two-point algorithm that solves the problem of clustering. Because of the nature of the steepest coordinate ascent algorithm avoiding the problem of clustering itself helps the improvement of convergence speed. The numerical examples show the performances of the new method is better than those of various steepest ascent algorithms.

• Journal of the military operations research society of Korea
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• v.9 no.1
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• pp.51-61
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• 1983

Lagrangian relaxation is used to the problem of scheduling jobs on unrelated parallel processors with the objective of minimizing makespan. The implicit condition for optimality is drawn out explicitly in order to apply the subgradient algorithm. To obtain the optimal solution, branch-and-bound-search method is devised. In the search, the special structure of the problem is exploited effectively, Some computational experiences with the algorithm are presented, and comparisons are made with the Land and Doig method.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.156-161
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• 1994

In this paper, we consider an optimal control problem of a nonlinear stochastic system. Dynamic programming approach is employed for the formulation of a stochastic optimal control problem. As an optimality condition, dynamic programming equation so called the Bellman equation is obtained, which seldom yields an analytical solution, even very difficult to solve numerically. We obtain the numerical solution of the Bellman equation using an algorithm based on the finite difference approximation and the contraction mapping method. Optimal controls are constructed through the solution process of the Bellman equation. We also construct a test case in order to investigate the actual performance of the algorithm.

• 한국정보통신설비학회:학술대회논문집
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• 2004.08a
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• pp.338-341
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• 2004

New concept of hybrid divisible load theory is introduced in this paper. Hybrid system deals with a combination of modularly divisible load and arbitrarily divisible load. Main idea of hybrid divisible load theory is introduced with a simple example. A condition of optimality is derived for the hybrid case.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.407-412
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• 2000

Response surface method is employed in optimizing the acoustic performance of automotive engine-cooling axial fans. The effects of modifications in blade geometry on noise reduction are investigated. Taking the far-field noise level as the objective, a quadratic response surface is constructed utilizing D-Optimality condition as the candidate-points selection criteria. It is shown that the quadratic model exhibits an excellent fitting capability resulting in the blade design with low far-field noise level.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.291-301
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• 1999

We study an optimal control problem of the fluid flow governed by the navier-Stokes equations. The control problem is formulated with the flow in the driven cavity. Existence of an optimal solution and first-order optimality condition of the optimal control are derived. We report the numerical results for the finite eleme수 approximations of the optimal solutions.

• 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.

• Structural Engineering and Mechanics
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• v.71 no.2
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• pp.119-129
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• 2019

Optimum shape and length of laterally loaded piles can be obtained with different optimization techniques. In particular, the Fully Stress Design method (FSD) is an optimality condition that allows to obtain the optimum shape of the pile, while the optimum length can be obtained through a transversality condition at the pile lower end. Using this technique, the structure is analysed by finite elements and shaped through the FSD method by contemporarily checking that the transversality condition is satisfied. In this paper it is noted that laterally loaded piles with optimum shape and length have some peculiar characteristics, depending on the type of cross-section, that allow to design them with simple calculations without using finite element analysis. Some examples illustrating the proposed simplified design method of laterally loaded piles with optimum shape and length are introduced.