• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.89-106
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• 2022

We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.2
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• pp.82-89
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• 1985

A new non-inferior solution is obtained by investigating method of weight p- norm to explain the conception of MCO (multiple criterion optimization) problem. And then the optimum non-inferior solution is obtained by the weight minimization method applied to objective function of MOSFET NAND rATEAlso this weight minimization method using weight P- norm methods can be applied to non-convex objective function. The result of this minimization method shows the efficiency in comparison with that of Lightner.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.12
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• pp.2271-2282
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• 2006

This paper is concerned with simulation issues arising in the PDE-based image restoration such as the total variation minimization(TVM) and its generalizations. In particular, we study the issues of staircasing and excessive dissipation of TVM-like smoothing operators. A strategy of scaling the algebraic system and a non-convex minimization are considered respectively for anti-staircasing and anti-diffusion. Furthermore, we introduce a variable constraint parameter to better preserve image edges. The resulting algorithm has been numerically verified to be efficient and reliable in denoising. Various numerical results are shown to confirm the claim.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.69-88
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• 2001

In the zigzag milling operation, an important issue is to design a machining strategy which minimizes the cutting time. An important variable for minimization of cutting time is the tool path length. The tool path is divided into cutting path and non-cutting path. Cutting path can be subdivided into tool path segment and step-over, and non-cutting path can be regarded as the tool retraction. We propose a new method to determine the cutting direction which minimizes the length of tool path in a convex or concave polygonal shape including islands. For the minimization of tool path length, we consider two factors such as step-over and tool retraction. Step-over is defined as the tool path length which is parallel to the boundary edges for machining area and the tool retraction is a non-cutting path for machining any remaining regions. In the determination of cutting direction, we propose a mathematical model and an algorithm which minimizes tool retraction length in complex shapes. With the proposed methods, we can generate a tool path for the minimization of cutting time in a convex or concave polygonal shapes including islands.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.7-13
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• 2004

A Conjugate Gradient (CG) algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and is designed for the minimization of general nonlinear functions. It compares favorably in numerical tests with the original Dixon algorithm on which the new algorithm is based.

• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.13-29
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• 2011

In this paper, we introduce the new concept of ${\omega}-D^*$-distance on a $D^*$-metric space and prove a non-convex minimization theorem which improves the result of Caristi[1], ${\'{C}}iri{\'{c}}$[2], Ekeland[4], Kada et al.[5] and Ume[8, 9].

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.589-600
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• 2016

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of m smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need O(mn) storage, where n is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only O(n) storage.

• Journal of Advanced Marine Engineering and Technology
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• v.37 no.7
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• pp.743-751
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• 2013

In this paper, an approach to deal with model uncertainty using norm-optimal iterative learning control (ILC) is mentioned. Model uncertainty generally degrades the convergence and performance of conventional learning algorithms. To deal with model uncertainty, a worst-case norm-optimal ILC is introduced. The problem is then reformulated as a convex minimization problem, which can be solved efficiently to generate the control signal. The paper also investigates the relationship between the proposed approach and conventional norm-optimal ILC; where it is found that the suggested design method is equivalent to conventional norm-optimal ILC with trial-varying parameters. Finally, simulation results of the presented technique are given.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.10
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• pp.4835-4855
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• 2018

In this paper, we study the sparse signal recovery that uses information of both support and amplitude of the sparse signal. A convergent iterative algorithm for sparse signal recovery is developed using Majorization-Minimization-based Non-convex Optimization (MM-NcO). Furthermore, it is shown that, typically, the sparse signals that are recovered using the proposed iterative algorithm are not globally optimal and the performance of the iterative algorithm depends on the initial point. Therefore, a modified MM-NcO-based iterative algorithm is developed that uses prior information of both support and amplitude of the sparse signal to enhance recovery performance. Finally, the modified MM-NcO-based iterative algorithm is used to estimate the time-varying sparse wireless channels with temporal correlation. The numerical results show that the new algorithm performs better than related algorithms.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2018.06a
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• pp.20-21
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• 2018

행렬의 rank 최소화 기법은 영상 잡음 제거, 행렬 완성(completion), low rank 행렬 복원 등 다양한 영상처리 분야에서 효과적으로 이용되어 왔다. 특히 nuclear norm 을 이용한 low rank 최소화 기법은 convex optimization 을 통하여 대상 행렬의 특이값(singular value)을 thresholding 함으로써 간단하게 low rank 행렬을 얻을 수 있다. 하지만, nuclear norm 을 이용한 low rank 최소화 방법은 행렬의 rank 값을 정확하게 근사하지 못하기 때문에 잡음 제거가 효과적으로 이루어지지 못한다. 본 논문에서는 영상의 잡음을 제거 하기 위해 다중 잡음 제거 영상을 이용하여 유사도가 높은 유사 패치 행렬을 구성하고, 유사 패치 행렬의 rank 를 non-convex function 을 이용하여 최소화시키는 방법을 통해 잡음을 제거하는 방법을 제안한다.