• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.267-280
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• 2017

In this paper, we study analytic and geometric properties of the solution q(z) to the differential equation q(z) + zq'(z)/q(z) = h(z) with the initial condition q(0) = 1 for a given analytic function h(z) on the unit disk |z| < 1 in the complex plane with h(0) = 1. In particular, we investigate the possible largest constant c > 0 such that the condition |Im [zf"(z)/f'(z)]| < c on |z| < 1 implies starlikeness of an analytic function f(z) on |z| < 1 with f(0) = f'(0) - 1 = 0.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.359-375
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• 2014

In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.

• Management Science and Financial Engineering
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• v.7 no.1
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• pp.41-56
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• 2001

This linear fractional - quadratic bilevel programming problem, in which the leader's objective function is a linear fractional function and the follower's objective function is a quadratic function, is studied in this paper. The leader's and the follower's variables are related by linear constraints. The derivations of the optimality conditions are based on Kuhn-Tucker conditions and the duality theory. It is also shown that the original linear fractional - quadratic bilevel programming problem can be solved by solving a standard linear fractional program and the optimal solution of the original problem can be achieved at one of the extreme point of a convex polyhedral formed by the new feasible region. The algorithm is illustrated with the help of an example.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1011-1023
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• 2010

In this paper we define the $L_p$-mixed curvature function of a convex body. We develop a formula connection the support function of $L_p$-mixed projection body with Fourier transform of the $L_p$-mixed curvature function. Using this formula we solve an analog of the Shephard projection problem for $L_p$-mixed projection bodies.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.9
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• pp.1972-1978
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• 2010

AAM(Active Appearance Model) is one of the most effective ways to detect deformable 2D objects and is a kind of mathematical optimization methods. The cost function is a convex function because it is a least-square function, but the search space is not convex space so it is not guaranteed that a local minimum is the optimal solution. That is, if the initial value does not depart from around the global minimum, it converges to a local minimum, so it is difficult to detect face contour correctly. In this study, an AAM-based face tracking algorithm is proposed, which is robust to various lighting conditions and backgrounds. Eye detection is performed using SIFT and Genetic algorithm, the information of eye are used for AAM's initial matching information. Through experiments, it is verified that the proposed AAM-based face tracking method is more robust with respect to pose and background of face than the conventional basic AAM-based face tracking method.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.959-982
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• 2015

In this study, a non-stationary random earthquake Clough-Penzien model is used to describe earthquake ground motion. Using stochastic direct integration in combination with an equivalent linear method, a solution is established to describe the non-stationary response of lead-rubber bearing (LRB) system to a stochastic earthquake. Two parameters are used to develop an optimization method for bearing design: the post-yielding stiffness and the normalized yield strength of the isolation bearing. Using the minimization of the maximum energy response level of the upper structure subjected to an earthquake as an objective function, and with the constraints that the bearing failure probability is no more than 5% and the second shape factor of the bearing is less than 5, a calculation method for the two optimal design parameters is presented. In this optimization process, the radial basis function (RBF) response surface was applied, instead of the implicit objective function and constraints, and a sequential quadratic programming (SQP) algorithm was used to solve the optimization problems. By considering the uncertainties of the structural parameters and seismic ground motion input parameters for the optimization of the bearing design, convex set models (such as the interval model and ellipsoidal model) are used to describe the uncertainty parameters. Subsequently, the optimal bearing design parameters were expanded at their median values into first-order Taylor series expansions, and then, the Lagrange multipliers method was used to determine the upper and lower boundaries of the parameters. Moreover, using a calculation example, the impacts of site soil parameters, such as input peak ground acceleration, bearing diameter and rubber shore hardness on the optimization parameters, are investigated.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.2
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• pp.3-13
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• 1993

In this study, we develop a B & B type algorithm for the concave minimization problem with 0-1 knapsack constraint. Our algorithm reformulates the original problem into the singly linearly constrained concave minimization problem by relaxing 0-1 integer constraint in order to get a lower bound. But this relaxed problem is the concave minimization problem known as NP-hard. Thus the linear function that underestimates the concave objective function over the given domain set is introduced. The introduction of this function bears the following important meanings. Firstly, we can efficiently calculate the lower bound of the optimal object value using the conventional convex optimization methods. Secondly, the above linear function like the concave objective function generates the vertices of the relaxed solution set of the subproblem, which is used to update the upper bound. The fact that the linear underestimating function is uniquely determined over a given simplex enables us to fix underestimating function by considering the simplex containing the relaxed solution set. The initial containing simplex that is the intersection of the linear constraint and the nonnegative orthant is sequentially partitioned into the subsimplices which are related to subproblems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.1
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• pp.189-196
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• 1990

In the present study, a new method of generating boundary-fitted coordinates systems controlled by control function is introduced. Application of the method to a three-dimensional simply-connected region is the demonstrated. The numerical grid generation has following feat ures, (a) The generated boundary fitted coordinates is well concentrated in near wall region and satisfied orthogonality, (b) The grid control function is fully automatic and well controlled in sharp convex boundary.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.881-893
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• 1997

E. M. Silvia introduced the class $S^\lambda_\alpha$ of $\alpha$-spirallike functions f(z) satisfying the condition $$ (A) Re[(e^{i\lambda} - \alpha) \frac{zf'(z)}{f(z)} + \alpha \frac{(zf'(z))'}{f'(z)}] > 0, $$ where $\alpha \geq 0, $\mid$\lambda$\mid$ < \frac{\pi}{2}$ and $$\mid$z$\mid$ < 1$. We will generalize Silvia class of functions by formally replacing f(z) in the denominator of (A) by a spirallike function g(z). We denote the new class of functions by $Y(\alpha,\lambda)$. In this note we obtain some results for the class $Y(\alpha,\lambda)$ including integral representation formula, relations between our class $Y(\alpha,\lambda)$ and Ziegler class $Z_\lambda$, the radius of convexity problem, a few coefficient estimates and a covering theorem for the class $Y(\alpha,\lambda)$.