• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.580-585
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• 2001

A response surface method(RSM) is utilized for structural optimization and implemented on a parametric CAD platform. Once an approximation of the performance function is made, no formal design sensitivity analysis is necessary. The approximation gives the designer the sensitivity information and furthermore intuition on the performance functions. The scheme for the design of experiment chosen for the RSM has a large influence on the accuracy of converged solutions and the amount of computation. The D-optimal design criterion as implemented in this paper is found efficient for the structural optimization. The program is developed on a parametric CAD platform and tested using several shape design problems of such as a torque arm and a belt clip. It is observed that the RSM used provides a faster convergence than other approximation methods for design sensitivity.

• 한국공간정보시스템학회:학술대회논문집
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• 2004.05a
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• pp.96-102
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• 2004

This study presents an effective stiffness-based optimal technique to control quantitatively lateral drift for 3-D steel frameworks subject to lateral loads. To this end, the displacement sensitivity depending on behavior characteristics of 3-D steel frameworks is established. Also, approximation concept that can preserve the generality of the mathematical programming and can efficiently solve large scale problems is introduced. Resizing sections in the stiffness-based optimal design are assumed to be uniformly varying in size. Two types of 30-story frames are presented to illustrate the features of the Quantitative lateral drift control technique proposed in this study.

• KIEE International Transaction on Systems and Control
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• v.12D no.1
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• pp.33-38
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• 2002

In this paper, the infinite time optimal regulation problem for weakly coupled bilinear systems with quadratic performance criteria is obtained by a sequence of algebraic Lyapunov equations. This is the new approach is based on the successive approximation. In particular, the order reduction is achieved by using suitable state transformation so that the original Lyapunov equations are decomposed into the reduced-order local Lyapunov equations. The proposed algorithms not only solve optimal control problems in the weakly coupled bilinear system but also reduce the computation time. This paper also includes an example to demonstrate the procedures.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.251-264
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• 2004

We introduce a semidiscrete mixed finite element approximation for the single-phase linear Stefan problem and show the unique existence of the approximation. And the optimal rate of convergence in $L^2$ and $H^1$ norms are derived.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.191-207
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• 2007

Based on a mixed Galerkin approximation, we construct the fully discrete approximations of $U_y$ as well as U to a single-phase quasilinear Stefan problem with a forcing term in non-divergence form. We prove the optimal convergence of approximation to the solution {U, S} and the superconvergence of approximation to $U_y$.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2617-2622
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• 2003

The pH neutralization process has long been taken as a representative benchmark problem of nonlinear chemical process control due to its nonlinearity and time-varying nature. For general nonlinear processes, it is difficult to control with a linear model-based control method so nonlinear controls must be considered. Among the numerous approaches suggested, the most rigorous approach is the dynamic optimization. However, as the size of the problem grows, the dynamic programming approach is suffered from the curse of dimensionality. In order to avoid this problem, the Neuro-Dynamic Programming (NDP) approach was proposed by Bertsekas and Tsitsiklis (1996). The NDP approach is to utilize all the data collected to generate an approximation of optimal cost-to-go function which was used to find the optimal input movement in real time control. The approximation could be any type of function such as polynomials, neural networks and etc. In this study, an algorithm using NDP approach was applied to a pH neutralization process to investigate the feasibility of the NDP algorithm and to deepen the understanding of the basic characteristics of this algorithm. As the global approximator, the neural network which requires training and k-nearest neighbor method which requires querying instead of training are investigated. The global approximator requires optimal control strategy. If the optimal control strategy is not available, suboptimal control strategy can be used even though the laborious Bellman iterations are necessary. For pH neutralization process it is rather easy to devise an optimal control strategy. Thus, we used an optimal control strategy and did not perform the Bellman iteration. Also, the effects of constraints on control moves are studied. From the simulations, the NDP method outperforms the conventional PID control.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.11
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• pp.1297-1308
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• 2011

The light-weight design of UTM (Urban Transit Maglev)-02 car-body frames are performed, based on initial configuration. The thicknesses of fourteen sub-structures are defined as design variables and the loading condition is considered according to weight of sub-structures, electronic and pneumatic modules and passengers. For efficient and robust process of design optimization, objective function and constraints are approximated by response surface approximation. Structural analysis is performed at some sampling points to construct the approximated objective function and constraints composed of design variables. Design space is changed to find many optimal candidates and best optimal design can be found eventually. The Matlab Optimization Toolbox is used to find optimal value and sensitivity analysis about each design variable is also performed.

• Transactions of Materials Processing
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• v.4 no.3
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• pp.214-221
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• 1995

In the paper, we have proposed a new method to determine the initial billet for the forged products using a function approximation in the neural network. The architecture of neural network is a three-layer neural network and the back propagation algorithm is employed to train the network. By utilizing the ability of function approximation of a neural network, an optimal billet is determined by applying the nonlinear mathematical relationship between the aspect ratios in the initial billet and the final products. The amount of incomplete filling in the die is measured by the rigid-plastic finite element method. The neural network is trained with the initial billet aspect ratios and those of the unfilled volumes. After learning, the system is able to predict the filling regions which are exactly the same or slightly different to the results of finite element simulation. This new method is applied to find the optimal billet size for the plane strain rib-web product in cold forging. This would reduce the number of finite element simulation for determining the optimal billet size of forging product, further it is usefully adapted to physical modeling for the forging design.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.207-220
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• 1999

In this paper, some of the issue about a group sequential method are considered in the Bayesian context. The continuous time optimal stopping boundary can be used to approximate the optimal stopping boundary for group sequential designs. The exact stopping boundary for group sequential design is obtained by using the backward induction method and is compared with the continuous optimal stopping boundary and the corrected continuous stopping boundary.