ISSN:
1432-5217
Keywords:
stationary point
;
variational inequality
;
fixed point algorithm
;
path-following
;
portfolio selection
;
traffic assignment
;
bi-matrix game
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract Given a setΩ ofR n and a functionf fromΩ intoR n we consider a problem of finding a pointx * inΩ such that(x−x *) t f(x *)≽0 holds for every pointx inΩ. This problem is called the stationary point problem and the pointx * is called a stationary point. We present a variable dimension algorithm for solving the stationary point problem with an affine functionf on a polytopeΩ defined by constraints of linear equations and inequalities. We propose a system of equations whose solution set contains a piecewise linear path connecting a trivial starting point inΩ with a stationary point. The path can be followed by solving a series of linear programs which inherit the structure of constraints ofΩ. The linear programs are solved efficiently with the Dantzig-Wolfe decomposition method by exploiting fully the structure.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01541030
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