Ellipsoidal approximation methods for variational inequalities over polyhedral set = 다면체에서의 변분부등식을 위한 타원근사해법

The application of variational inequalities covers a great number of areas. We concern with numerical solution method of the variational inequality over a polyhedral set. Among well known numerical methods are the projection method, Newton method and etc. The subproblems of them, however, require another iterative methods which are themselves often computationally challenging since they are also optimization problems. The purpose of this research is to propose effective methods to solve these subproblems by approximating the given set K via an inscribed ellipsoid. We propose an ellipsoidal projection method and an ellipsoidal Newton method. The subproblems of them are shown to be solved in a closed form. A custom tailored version of the proposed ellipsoidal projection method for fixed demand traffic equilibrium problem is also proposed. A practical version of the ellipsoidal projection method with additional line search step is proposed to give safety against possible risk of small step size. Convergence properties of the above methods are investigated. Limited computational experiments with small sized traffic equilibrium problems show that the proposed ellipsoidal projection method is promising.
Advisors
Ahn, Byong-Hunresearcher안병훈researcher
Publisher
한국과학기술원
Issue Date
1993
Identifier
68141/325007 / 000805121
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 경영과학과, 1993.8, [ iii, 119 p. ]

URI
http://hdl.handle.net/10203/43733
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=68141&flag=t
Appears in Collection
MG-Theses_Ph.D.(박사논문)
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