• Proceedings of the Korean Society of Medical Physics Conference
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• 2005.04a
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• pp.79-82
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• 2005

In this study, we have tested the feasibility of the convex non-linear objective model and the line search optimization method for the fluence map optimization (FMO). We've created the convex nonlinear objective function with simple bound constraints and attained the optimal solution using well-known gradient algorithms with an Armijo line search that requires sufficient objective function decrease. The algorithms were applied to 10 head-and-neck cases. The numbers of beamlets were between 900 and 2,100 with a 3 mm isotropic dose grid. Nonlinear optimization methods could efficiently solve the IMRT FMO problem in well under a minute with high quality for clinical cases.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1025-1039
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• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.4
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• pp.279-283
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• 2005

This paper deals with the design of a low-order H/sub ∞/ controller by using an iterative linear matrix inequality (LMI) method. The low-order H/sub ∞/ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, the recently developed penalty function method is applied. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. Numerical experiments showed the effectiveness of the proposed algorithm.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.585-604
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• 2012

In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.5
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• pp.102-109
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• 1985

A new yield maximization procedure by investigating method of the multidimensional Monte Carlo integration is presented. And then maximum yield is obtained by the new modified weight selection algorithm applied to objective function of MOSFET NAND GATE Also this yield maximization procedure can be applied to nonconvex objective function.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.8
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• pp.1491-1497
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• 2007

This paper considers robust and non-fragile guaranteed cost controller design method for descriptor systems with parameter uncertainties and time delay, and static state feedback controller with gain variations. The existence condition of controller, the design method of controller, the upper bound to minimize guaranteed cost function, and the measure of non-fragility in controller are proposed using linear matrix inequality (LMI) technique, which can be solved efficiently by convex optimization. Therefore, the presented robust and non-fragile guaranteed cost controller guarantees the asymptotic stability and non-fragility of the closed loop systems in spite of parameter uncertainties, time delay, and controller fragility.

• Journal of Multimedia Information System
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• v.1 no.1
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• pp.87-93
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• 2014

The aim of microscopic image restoration is to recover the image by applying the inverse process of degradation, and the results facilitate automated and improved analysis of the image. In this work, we consider the problem of image restoration as a minimization problem of convex cost function, which consists of a least-squares fitting term and regularization terms with non-negative constraints. The finite step method is proposed to solve this constrained convex optimization problem. We demonstrate the convergence of this method. Efficiency and restoration capability of the proposed method were tested and illustrated through numerical experiments.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.227-232
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• 1992

In this paper we prove that if (.ohm., .SIGMA., .mu.) is a non-purely atomic measure space and X is strictly convex, then X has the asymptotic-norming property II if and only if $L_{p}$ (X, .mu.), 1 < p < .inf., has the asymptotic-norming property II. And we prove that if $X^{*}$ is an Asplund space and strictly convex, then for any p, 1 < p < .inf., $X^{*}$ has the .omega.$^{*}$-ANP-II if and only if $L_{p}$ ( $X^{*}$, .mu.) has the .omega.$^{*}$-ANP-II.*/-ANP-II.

• 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 Biomedical Engineering Research
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• v.36 no.5
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• pp.211-220
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• 2015

Recently, model-based iterative reconstruction (MBIR) has played an important role in transmission tomography by significantly improving the quality of reconstructed images for low-dose scans. MBIR is based on the penalized-likelihood (PL) approach, where the penalty term (also known as the regularizer) stabilizes the unstable likelihood term, thereby suppressing the noise. In this work we further improve MBIR by using a more expressive regularizer which can restore the underlying image more accurately. Here we used a spline regularizer derived from a linear combination of the two-dimensional splines with first- and second-order spatial derivatives and applied it to a non-quadratic convex penalty function. To derive a PL algorithm with the spline regularizer, we used a separable paraboloidal surrogates algorithm for convex optimization. The experimental results demonstrate that our regularization method improves reconstruction accuracy in terms of both regional percentage error and contrast recovery coefficient by restoring smooth edges as well as sharp edges more accurately.