• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• 대한전기학회논문지:전력기술부문A
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• 제52권9호
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• pp.550-556
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• 2003

Price-based unit commitment is one of bidding strategies which a Genco may take in a practical manner. For that purpose, it is required for a Genco to decide output levels of its generators at each trade period. In this paper, an economic dispatch of thermal units is proposed considering the quantity of reserve contracts. A gradient projection algorithm is adopted as an optimization tool. A direct form of a projection matrix without any calculation of matrix inverse and multiplications is induced. Besides, it is proved that there is no need to check one of the two optimality conditions in the gradient projection method, which also requires matrix inverse and multiplications.

• 한국생산제조학회지
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• 제5권4호
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• pp.74-81
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• 1996

This paper is to estimate sizing design sensitivity of linear and nonlinear vehicle frame structure using structural ananlysis result from ANSYS. Using design sensitivity results, optimal design of plane vehicle frame structure with buckling constraint is carried out the gradient projection method. Optimal design results are compares gradient projection method resrult with SUMT result.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1994년도 봄 학술발표회 논문집
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• pp.38-45
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• 1994

The general conceptual constitution of structural optimization is formulated. The algorithm using the gradient projection method and design sensitivity analysis is discussed. Examples of minimum-weight design for six-story steel plane frame are taken to illustrate the application of this algorithm. The advantages of this algorithm such as marginal cost and design sensitivity analysis as well as system analysis are explained.

• 대한수학회지
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• 제56권4호
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• 전산구조공학
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• 제8권4호
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• pp.99-106
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• 1995

구조물의 최적설계에 대한 일반적인 개념이 제시되며 Gradient Projection법과 설계민감도 해석을 사용한 최적화 알고리즘이 논의된다. 6층 평면 철골 구조물의 최소무게설계의 예를 통해 이 알고리즘의 적용을 예시한다. 시스템 전체의 비용분석뿐만 아니라 임계 비용 및 설계민감도 해석과 같은 이 알고리즘의 장점에 관하여 설명한다.

• 대한교통학회지
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• 제18권5호
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• pp.99-107
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• 2000

경로기반 통행 배정은 실시간 통행 배정에서 이용되는 경로기반 해를 제공할 수 있기 때문에 첨단 교통 체계(ITS)의 실시간 교통 제어 및 교통 안내 등에 유용하게 이용될 수 있다. 많이 사용되고 있는 경로기반 통행배정 알고리즘의 하나인 Gradient Projection(GP) 알고리즘은 일반적으로 최적해 근처로는 빠른 접근 속도를 보이나. 일단 최적해에 근접하면 수렴 속도가 다소 느려지게되는 단점이 있다. 기존 알고리즘의 이러한 단점을 극복하기 위해 기존의 GP 알고리즘에 Conjugate Gradient 법을 결합시켜 보다 효율적인 경로기반 통행배정 알고리즘을 구축하였다. 이는 최적해 근처에서 더욱 정확한 이동방향을 결정하여 빠른 시간 내에 최적해를 도출해 내도록 하기 위한 것이다. 또한, 구축된 알고리즘을 가로망에 적용, 그 효율성을 검증하여 Conjugate Gradient 법이 통행 배정 모형의 사용자 평형 모형에서와 같은 목적함수의 경우에서도 매우 빠른 수렴을 위해 유용하게 쓰일 수 있다는 것을 보였다.

• Structural Engineering and Mechanics
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• 제65권6호
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• pp.707-719
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• 2018

In this article, a new method is introduced to improve the local search capability of meta-heuristic algorithms using the projection of the path on the border of constraints. In a mathematical point of view, the Gradient Projection Method is applied through a new approach, while the imposed limitations are removed. Accordingly, the gradient vector is replaced with a new meta-heuristic based vector. Besides, the active constraint identification algorithm, and the projection method are changed into less complex approaches. As a result, if a constraint is violated by an agent, a new path will be suggested to correct the direction of the agent's movement. The presented procedure includes three main steps: (1) the identification of the active constraint, (2) the neighboring point determination, and (3) the new direction and step length. Moreover, this method can be applied to some meta-heuristic algorithms. It increases the chance of convergence in the final phase of the search process, especially when the number of the violations of the constraints increases. The method is applied jointly with the authors' newly developed meta-heuristic algorithm, entitled Star Graph. The capability of the resulted hybrid method is examined using the optimal design of truss and frame structures. Eventually, the comparison of the results with other meta-heuristics of the literature shows that the hybrid method is successful in the global as well as local search.

• 한국통신학회논문지
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• 제29권10C호
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• pp.1402-1413
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• 2004

비강체 (non-rigid) 영상 등록에서 추정되는 좌표변환은 가역이어야 함으로 그 변환의 Jacobian 행렬식은 항상 양수 값을 가져야 한다. 본 논문에서는 이러한 가역 조건을 만족하는 좌표변환의 조건을 gradient 크기 제한의 조건으로 구한다. 또한 cubic B-spline을 이용한 변환 모델의 경우, 이 gradient 크기 제한 조건을 만족시키는 인수 집합을 이웃한 두 계수들의 차이가 제한된 인수들의 집합으로 구하였다. 이러한 인수들의 집합은 half space들의 교집합으로 이루어진 convex 집합이다. 본 논문에서는 이 convex 집합에 속하는 인수로 구성되는 좌표변환들 중에서 유사지수 (similarity measure) 를 최대로 만드는 변환을 gradient projection 최적화 기법을 통해 발견하였다. 이론적 분석, 폐 CT (Computed Tomography) 영상을 이용한 시뮬레이션 및 실험을 통하여, 제안된 알고리즘의 성능이 벌칙 함수 penalty function) 를 이용하는 기존의 방법보다 우수함을 증명하였다.

• 한국경영과학회지
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• 제6권2호
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• pp.25-34
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• 1981

In this paper, we propose a non-edge following method for linear programs. Unlike alledged poor performance of algorithms of this type, this method performs well at least with 25 randomly generated problems. This method is comparable to Rosen's gradient projection method as applied to the dual formulation. The latter is of general purpose, and no implementation rules are available for linear program applications. This paper suggests ways of finding improving dual feasible directions, and of allowing to move across the extreme faces of a higher dimension polyhedron. Rather simple computational rules are provided for projection operations needed at each iteration.