• Communications for Statistical Applications and Methods
• /
• 제20권3호
• /
• pp.225-233
• /
• 2013

The linear support vector machine(SVM) is motivated by the maximal margin separating hyperplane and is a popular tool for binary classification tasks. Many studies exist on the consistency properties of SVM; however, it is unknown whether the linear SVM is consistent for estimating the optimal classification boundary even in the simple case of two Gaussian classes with a common covariance, where the optimal classification boundary is linear. In this paper we show that the linear SVM can be inconsistent in the univariate Gaussian classification problem with a common variance, even when the best tuning parameter is used.

• Journal of applied mathematics & informatics
• /
• 제17권1_2_3호
• /
• pp.315-328
• /
• 2005

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

• 전기의세계
• /
• 제21권3호
• /
• pp.48-52
• /
• 1972

The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

• Structural Engineering and Mechanics
• /
• 제6권6호
• /
• pp.633-641
• /
• 1998

Finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates with various types of internal line supports. These plates are subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load. This is achieved by determining the fibre orientations optimally with the effects of bending-twisting coupling taken into account. The finite element method coupled with an optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of internal line support type and boundary conditions on the optimal ply angles and the buckling load are numerically studied. The laminate behavior with respect to fibre orientation changes significantly in the presence of internal line supports as compared to that of a laminate where there is no internal supporting. This change in behavior has significant implications for design optimisation as the optimal values of design variables with or without internal supporting differ substantially.

• 대한수학회보
• /
• 제48권4호
• /
• pp.791-812
• /
• 2011

This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European option can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up until now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These approaches typically provide numerical or approximate analytic methods to find the price and the boundary. Topics included in this survey are early approaches(trees, finite difference schemes, and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, analytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochastic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.

• 대한원격탐사학회지
• /
• 제25권3호
• /
• pp.295-309
• /
• 2009

In this study, an iterative maximum a posteriori (MAP) approach using a Bayesian model of Markovrandom field (MRF) was proposed for despeckling images that contains speckle. Image process is assumed to combine the random fields associated with the observed intensity process and the image texture process respectively. The objective measure for determining the optimal restoration of this "double compound stochastic" image process is based on Bayes' theorem, and the MAP estimation employs the Point-Jacobian iteration to obtain the optimal solution. In the proposed algorithm, MRF is used to quantify the spatial interaction probabilistically, that is, to provide a type of prior information on the image texture and the neighbor window of any size is defined for contextual information on a local region. However, the window of a certain size would result in using wrong information for the estimation from adjacent regions with different characteristics at the pixels close to or on boundary. To overcome this problem, the new method is designed to use less information from more distant neighbors as the pixel is closer to boundary. It can reduce the possibility to involve the pixel values of adjacent region with different characteristics. The proximity to boundary is estimated using a non-uniformity measurement based on standard deviation of local region. The new scheme has been extensively evaluated using simulation data, and the experimental results show a considerable improvement in despeckling the images that contain speckle.

• East Asian mathematical journal
• /
• 제22권2호
• /
• pp.171-188
• /
• 2006

We consider the problem of an optimal control of the wave equation with a localized nonlinear dissipation. An optimal control is used to bring the state solutions close to a desired profile under a quadratic cost of control. We establish the existence of solutions of the underlying initial boundary value problem and of an optimal control that minimizes the cost functional. We derive an optimality system by formally differentiating the cost functional with respect to the control and evaluating the result at an optimal control.

• East Asian mathematical journal
• /
• 제1권
• /
• pp.101-112
• /
• 1985

• Smart Structures and Systems
• /
• 제16권6호
• /
• pp.1023-1047
• /
• 2015

In this study, the optimal location of the MR fluid segments in a partially treated laminated composite sandwich plate has been identified to maximize the natural frequencies and the loss factors. The finite element formulation is used to derive the governing differential equations of motion for a partially treated laminated composite sandwich plate embedded with MR fluid and rubber material as the core layer and laminated composite plate as the face layers. An optimization problem is formulated and solved by combining finite element analysis (FEA) and genetic algorithm (GA) to obtain the optimal locations to yield maximum natural frequency and loss factor corresponding to first five modes of flexural vibration of the sandwich plate with various combinations of weighting factors under various boundary conditions. The proposed methodology is validated by comparing the natural frequencies evaluated at optimal locations of MR fluid pockets identified through GA coupled with FEA and the experimental measurements. The converged results suggest that the optimal location of MR fluid pockets is strongly influenced not only by the boundary conditions and modes of vibrations but also by the objectives of maximization of natural frequency and loss factors either individually or combined. The optimal layout could be useful to apply the MR fluid pockets at critical components of large structure to realize more efficient and compact vibration control mechanism with variable damping.

• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 2002년도 춘계학술대회 논문집
• /
• pp.77-81
• /
• 2002

A new method of optimal blank shape design using the initial nodal velocity (INOV) has been proposed for the drawings of arbitrary shaped cups. With the given information of tool shape and the final product shape, corresponding initial blank shape has been found from the motion of boundary nodes. Although the sensitivity method, the past work of Hynbo Shim and Kichan Son, has been proved to be excellent method to find optimal blank shapes, the method has a problem that a couple of deformation analysis is required at each design step and it also exhibits an abnormal behaviors in the rigid body rotation prevailing region. In the present method INOV, only a single deformation analysis per each design stage is required. Drawings of practical products as well as oil-pan have been chosen as the examples. At every case the optimal blank shapes have been obtained only after a few times of modification without predetermined deformation path. The deformed shape with predicted optimal blank almost coincides with the target shape at every case. Through the investigation the INOV is found to be very effective in the arbitrary shaped drawing process design.