• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.53-56
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• 2000

The problem ( Ρ ) of optimizing a linear function d$\^$T/x over the set of efficient set for a multiple objective linear program ( Μ ) is difficult because the efficient set is nonconvex. There some interesting properties between the objective linear vector ｄ and the matrix of multiple objectives C and those properties lead us to establish criteria to solve ( Ρ ) with a linear program. In this paper we investigate a system of the linear equations C$\^$T/${\alpha}$=d and construct two linearly independent positive vectors ${\mu}$, ν such that ${\alpha}$=${\mu}$-ν. From those vectors ${\mu}$, ν, solving an weighted sum linear program for finding an efficient extreme point for the ( Μ ) is a way to get an optimal solution ( Ρ ). Therefore our theory gives an easy way of solving nonconvex program ( Ρ ) with a weighted sum linear program.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.265-283
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• 2022

MovieLens data consists of recorded movie evaluations that was often used to measure the evaluation score in the recommendation system research field. In this paper, we provide additional information obtained by clustering user-specific genre preference information through movie evaluation data and movie genre data. Because the number of movie ratings per user is very low compared to the total number of movies, the missing rate in this data is very high. For this reason, there are limitations in applying the existing clustering methods. In this paper, we propose a convex clustering-based method using the pairwise fused penalty motivated by the analysis of MovieLens data. In particular, the proposed clustering method execute missing imputation, and at the same time uses movie evaluation and genre weights for each movie to cluster genre preference information possessed by each individual. We compute the proposed optimization using alternating direction method of multipliers algorithm. It is shown that the proposed clustering method is less sensitive to noise and outliers than the existing method through simulation and MovieLens data application.

• Journal of the Korea Concrete Institute
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• v.20 no.5
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• pp.627-634
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• 2008

This paper presents an optimum mixture design method for proportioning a concrete. In the proposed method, the search space is constrained as the domain defined by the minimal convex region of a database, instead of the available range of each component and the ratio composed of several components. The model for defining the search space which is expressed by the effective region is proposed. The effective region model evaluates whether a mix-proportion is effective on processing for optimization, yielding highly reliable results. Three concepts are adopted to realize the proposed methodology: A genetic algorithm for the optimization; an artificial neural network for predicting material properties; and a convex hull for evaluating the effective region. And then, it was applied to an optimization problem wherein the minimum cost should be obtained under a given strength requirement. Experimental test results show that the mix-proportion obtained from the proposed methodology using convex hulls is found to be more accurate and feasible than that obtained from a general optimum technique that does not consider this aspect.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.2
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• pp.130-135
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• 2004

This paper presents a new design methods of the short-term load forecasting system (STLFS) using the data mining. The structure of the proposed STLFS is divided into two parts: the Takagi-Sugeno (T-S) fuzzy model-based classifier and predictor The proposed classifier is composed of the Gaussian fuzzy sets in the premise part and the linearized Bayesian classifier in the consequent part. The related parameters of the classifier are easily obtained from the statistic information of the training set. The proposed predictor takes form of the convex combination of the linear time series predictors for each inputs. The problem of estimating the consequent parameters is formulated by the convex optimization problem, which is to minimize the norm distance between the real load and the output of the linear time series estimator. The problem of estimating the premise parameters is to find the parameter value minimizing the error between the real load and the overall output. Finally, to show the feasibility of the proposed method, this paper provides the short-term load forecasting example.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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• pp.557-562
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• 2004

This paper deals with a robust mixed ${H_2}/{H_{\infty}}$ filter design problem for a nonlinear dynamic system modeled as a T-S fuzzy system. Integral quadratic constraints are used to describe various kinds of uncertainties of the plant. A sufficient condition for solvability is given in terms of linear matrix inequality problem which can be efficiently solved using a convex optimization technique. In order to demonstrate the Proposed method, a numerical design example is provided.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1229-1244
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• 2017

In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2015.11a
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• pp.81-83
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• 2015

객관적 영상 화질 측정(Image Quality Assessment: IQA)방법은 영상 화질 최적화 문제해결을 목적으로 하는 영상 처리 및 컴퓨터 비전 분야에 매우 중요하게 사용된다. 이를 위해, 저복잡도, 고성능 및 좋은 수학적 특성(예를 들어, 척도성(metricability), 미분가능성(differentiability) 및 볼록 성질(convexity))을 모두 만족시키는 객관적 IQA 방법이 활발히 연구되어 왔다. 그러나, 위해 위에서 언급한 좋은 수학적 특성을 가지는 대부분의 객관적 IQA 방법들은 좋은 수학적 특성을 만족시키기 위해 상당한 예측성능의 감소를 초래했다. 본 논문은 위에서 언급한 좋은 수학적 특성을 모두 만족시키면서, 예측 성능이 향상된 새로운 IQA 방법을 제안한다. 인간 시각 체계의 감수영역은 광도 입력에 대해 공간 도메인에서 미분 형태의 응답을 가지므로, 제안 방법은 이러한 시각 체계 응답을 모방하여 기울기 연산자를 도입한다. 제안한 방법에서 도입한 기울기 연산자는 매우 단순하게 설계되어, 계산 복잡도가 매우 낮다. 광범위한 실험 결과, 제안하는 IQA 방법은 기존 수학적 특성이 좋은 IQA 방법들 대비 더 좋은 성능을 보이면서 계산 복잡도 또한 낮았다. 따라서 제안 IQA 방법은 다양한 영상 화질 최적화 문제에 매우 효과적으로 적용될 수 있다.

• Journal of Korean Society of Steel Construction
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• v.10 no.4 s.37
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• pp.657-666
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• 1998

This study presents an effective dual algorithm for the optimal design of steel structures with displacement constraints. The dual method can replace a primary optimization problem with a sequence of approximate explicit subproblems with a simple algebraic structure. Since being convex and separable, each subproblem can be solved efficiently by the dual method. Specifically, this study uses the principle of virtual work to obtain the displacement constraint equations with an explicit form and adds the linear regression equation expressing the relationships between the cross-section properties to the dual algorithm to reduce the number of design variables. Furthermore, this study deals with the discrete optimization problem to select members with the standard steel sections. Through numerical analyses, the proposed method will be compared with the conventional optimality criteria method.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.5
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• pp.155-162
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• 2015

This paper proposes a deterministic optimization algorithm to solve economic load dispatch problem with quadratic convex fuel cost function. The proposed algorithm primarily partitions a generator with prohibited zones into multiple generators so as to place them afield the prohibited zone. It then sets initial values to $P_i{\leftarrow}P_i^{max}$ and reduces power generation costs of those incurring the maximum unit power cost. It finally employs a swap optimization process of $P_i{\leftarrow}P_i-{\beta}$, $P_j{\leftarrow}P_j+{\beta}$ where $_{max}\{F(P_i)-F(P_i-{\beta})\}$ > $_{min}\{F(P_j+{\beta})-F(P_j)\}$, $i{\neq}j$, ${\beta}=1.0,0.1,0.01,0.001$. When applied to 3 different 15-generator cases, the proposed algorithm has consistently yielded optimized results compared to those of heuristic algorithms.

• Journal of Korean Society of Transportation
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• v.18 no.1
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• pp.61-73
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• 2000

The equilibrium network design problem can be formulated as a mathematical Program with variational inequality constraints. We know this problem may have may multiple local solutions due to its inherent characteristics - Nonlinear Objective function and Nonlinear, Nonconvex constraints. Hence, it is difficult to solve for a globally optimal solution. In this paper, we propose a genetic algorithm to obtain a globa1 optimum among many local optima. A Proposed a1gorithm is compared with 4 different solution algorithms for 1 small test network and 1 real-size network. The results of some computational testing are reported.