• Journal of the Korean Institute of Telematics and Electronics
• /
• v.22 no.2
• /
• pp.82-89
• /
• 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
• /
• v.10 no.12
• /
• pp.2271-2282
• /
• 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
• /
• v.27 no.1
• /
• pp.69-88
• /
• 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.

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

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

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.3
• /
• pp.107-116
• /
• 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.

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

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.325-331
• /
• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.461-466
• /
• 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.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.1051-1067
• /
• 2023

In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established.