• ETRI Journal
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• 제24권3호
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• pp.239-246
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• 2002

We investigate an alternative blind adaptive multiuser detection scheme based on a non-canonical linearly constrained constant modulus (LCCM) criterion and prove that, under the constrained condition, the non-canonical linearly constrained constant modulus algorithm (LCCMA) can completely remove multiple -access interference. We further demonstrate that the non-canonical LCCM criterion function is strictly convex in the noise-free state, and that under the constrained condition, it is also strictly convex even where small noise is present. We present a simple method for selecting the constant as well as a stochastic gradient algorithm for implementing our scheme. Numerical simulation results verify the scheme's efficiency.

• 한국컴퓨터정보학회논문지
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• 제19권8호
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• pp.55-62
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• 2014

게임이론을 적용하여 에너지 효율적인 전송률 스케줄링 방안을 제안한다. 먼저, 개별 단말의 효용함수를 정의하고, 효용함수를 최적화하도록 에너지를 결정하는 비협력적 전송률 게임을 모델링한다. 여기서, 효용함수는 개별 단말이 데이터 전송시 소모하는 전송 에너지이다. 특히, 개별 단말의 효용함수가 Convex 함수임을 이용하여 에너지 효율적인 전송률 스케줄링 문제가 나쉬 평형이 존재함을 증명하고, 이를 기반으로 비협력적 스케줄링 알고리즘을 제안한다. 또한, 에너지 효율의 개선을 위해서 개별 단말의 효용함수의 합을 최적화하는 협력적 스케줄링 알고리즘도 제안한다. 성능 분석을 위하여 비협력적 알고리즘과 협력적 알고리즘의 수렴도 결과와 에너지 효율성 결과를 제시한다.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1999년도 춘계학술대회 논문집
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• pp.141-146
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• 1999

A new method, so called MMA(Method of Moving Asymptotes) was applied to the optimization problems of non-linear functions and non-linear structures. In each step of the iterative process, tile MMA generates a strictly convex approximation subproblems and solves them by using the dual problems. The generation of these subproblems is controlled by so called 'moving asymptotes', which may both make no oscillation and speed up tile convergence rate of optimization process. By contrast in generalized dual function, the generated function by MMA is always explicit type. Both the objective and behaviour constraints which were approximated are optimized by dual function. As the results of some examples, it was found that this method is very effective to obtain the global solution for problems with many local solutions. Also it was found that MMA is a very effective approximate method using the original function and its 1st derivatives.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권3호
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• pp.107-116
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• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.

• 대한기계학회논문집A
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• 제27권8호
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• pp.1353-1362
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• 2003

This paper considers a simultaneous optimization problem of structure and control systems. The problem is generally formulated as a non-convex optimization problem for the design parameters of mechanical structure and controller. Therefore, it is not easy to obtain the global solutions for practical problems. In this paper, we parameterize all design parameters of the mechanical structure such that the parameters work in the control system as decentralized static output feedback gains. Using this parameterization, we have formulated a simultaneous optimization problem in which the design specification is defined by the Η$_2$and Η$\_$$\infty$/ norms of the closed loop transfer function. So as to lead to a convex problem we approximate the nonlinear terms of design parameters to the linear terms. Then, we propose a convex optimization method that is based on linear matrix inequality (LMI). Using this method, we can surely obtain suboptimal solution for the design specification. A numerical example is given to illustrate the effectiveness of the proposed method.

• Communications for Statistical Applications and Methods
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• 제19권5호
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• pp.655-662
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• 2012

Classification is an important research field in pattern recognition with high-dimensional predictors. The support vector machine(SVM) is a penalized feature selector and classifier. It is based on the hinge loss function, the non-convex penalty function, and the smoothly clipped absolute deviation(SCAD) suggested by Fan and Li (2001). We developed the algorithm for the multiclass SVM with the SCAD penalty function using the local quadratic approximation. For multiclass problems we compared the performance of the SVM with the $L_1$, $L_2$ penalty functions and the developed method.

• 호남수학학술지
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• 제35권1호
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• pp.37-49
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• 2013

Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

• Communications for Statistical Applications and Methods
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• 제22권2호
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• pp.147-157
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• 2015

We consider a sparse high-dimensional linear regression model. Penalized methods using LASSO or non-convex penalties have been widely used for variable selection and estimation in high-dimensional regression models. In penalized regression, the selection and prediction performances depend on which penalty function is used. For example, it is known that LASSO has a good prediction performance but tends to select more variables than necessary. In this paper, we propose an additive sparse penalty for variable selection using a combination of LASSO and minimax concave penalties (MCP). The proposed penalty is designed for good properties of both LASSO and MCP.We develop an efficient algorithm to compute the proposed estimator by combining a concave convex procedure and coordinate descent algorithm. Numerical studies show that the proposed method has better selection and prediction performances compared to other penalized methods.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.461-466
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• 2006

In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

• Management Science and Financial Engineering
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• 제12권1호
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• pp.113-125
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• 2006

Bilevel programming problem is a two-stage optimization problem where the constraint region of the first level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel quadratic/linear fractional programming problem in which the objective function of the first level is quasiconcave, the objective function of the second level is linear fractional and the feasible region is a convex polyhedron. Considering the relationship between feasible solutions to the problem and bases of the coefficient submatrix associated to variables of the second level, an enumerative algorithm is proposed which finds a global optimum to the problem.