• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.4
• /
• pp.162-172
• /
• 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.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 1998.06a
• /
• pp.91-94
• /
• 1998

본 논문에서는 블록간, 블록 내수, 수평. 수직 방향성, 그리고 시간 영역의 정보를 이용하는 압축 동영상의 블록화 및 링 현상을 제거하는 방식을 제안한다. 위의 정보를 이용하여 새로운 부가 함수가 정의되며, 최적 해를 구하기 위해 gradient와 projection을 결합시킨 hybrid 형태의 기법을 이용한다. 또한, 정규화 계수들 및 projection을 위한 영역의 설정을 부호화단에서는 이용 가능한 정보로부터 추출하게 되므로 계산량을 감소시킬 수 있다. 실험 결과로부터 제안된 방식의 효율성을 확인할 수 있다.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.52 no.9
• /
• pp.550-556
• /
• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1994.04a
• /
• pp.38-45
• /
• 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.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.5 no.4
• /
• pp.74-81
• /
• 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.

• Computational Structural Engineering
• /
• v.8 no.4
• /
• pp.99-106
• /
• 1995

The General conceptual constitution of structural optimization is formulated and 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 applicability of this algorithm. The advantages of this algorithm such as marginal cost and design sensitivity analysis as well as system analysis are explained.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.1001-1016
• /
• 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.

• Journal of the Optical Society of Korea
• /
• v.20 no.1
• /
• pp.118-124
• /
• 2016

The shape and location of the cutoff shield in a projection-type headlight system were optimized by a ray-tracing technique. A shield based on a Petsval surface showed better cutoff characteristics than a flat or cylindrical shield, such as a sharp intensity gradient and less color separation at the cutoff line. Adjustment of the shield’s location between the reflector and the aspheric lens further improved its cutoff characteristics.

• Journal of Broadcast Engineering
• /
• v.3 no.2
• /
• pp.172-179
• /
• 1998

본 논문에서는 hybrid MC/DCT 기법을 이용한 압축 영상의 블록화 및 링 현상을 동시에 제거하는 기법이 제안된다. 압축 영상의 블록화 링 현상은 블록간, 블록 내에서 다른 특성이 있고, 수평. 수직 방향의 상관 관계에 따라 다를 수 있으며, 영상 사이의 일정 상관 관계에 따라 다르게 형성된다. 본 논문에서는 이러한 블록간, 블록 내부, 수평수직 방향성, 그리고 시간 영역의 정보를 이용하여 새로운 부가 완화 함수를 정의하며, 최적 해를 구하기 위해 gradient와 양자화 과정으로부터 설정할 수 있는 비선형 연산을 이용한 projection을 결합시킨 hybrid 형태의 기법이 제안된다. 또한, 정규화 계수들은 부호화단에서 이용 가능한 정보로부터 예측하여 기존 방식이 있던 계산량이 이득을 얻을 수 있다. 실험 결과로부터 제안된 방식의 주관적, 객관적 성능 향상을 확인할 수 있었다.

• Journal of Korean Society of Transportation
• /
• v.18 no.5
• /
• pp.99-107
• /
• 2000

Path-based assignment(PBA) is valuable to dynamic traffic control and routing in integrated ITS framework. As one of widely studied PBA a1gorithms, Gradient Projection(GP) a1gorithm typically fields rapid convergence to a neighborhood of an optimal solution. But once it comes near a solution, it tends to slow down. To overcome this problem, we develop more efficient path-based assignment algorithm by combining Conjugate Gradient method with GP algorithm. It determines more accurate moving direction near a solution in order to gain a significant advantage in speed of convergence. Also this algorithm is applied to the Sioux-Falls network and verified its efficiency. Then we demonstrate that this type of method is very useful in improving speed of convergence in the case of user equilibrium problem.