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Dinkelbach's algorithm was developed to solve convex fractinal programming. This method achieves the optimal solution of the
optimisation problem by means of solving a sequence of non-linear convex programming subproblems defined by a parameter.
In this paper it is shown that Dinkelbach's algorithm can be used to solve general fractional programming. The applicability
of the algorithm will depend on the possibility of solving the subproblems.
Dinkelbach's extended algorithm is a framework to describe several algorithms which have been proposed to solve linear fractional
programming, integer linear fractional programming, convex fractional programming and to generate new algorithms. The applicability
of new cases as nondifferentiable fractional programming and quadratic fractional programming has been studied.
We have proposed two modifications to improve the speed-up of Dinkelbachs algorithm. One is to use interpolation formulae
to update the parameter which defined the subproblem and another truncates the solution of the suproblem. We give sufficient
conditions for the convergence of these modifications.
Computational experiments in linear fractional programming, integer linear fractional programming and non-linear fractional
programming to evaluate the efficiency of these methods have been carried out. 相似文献
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The general problem of estimating origin–destination (O–D) matrices in congested traffic networks is formulated as a mathematical programme with equilibrium constraints, referred to as the demand adjustment problem (DAP). This approach integrates the O–D matrix estimation and the network equilibrium assignment into one process. In this paper, a column generation algorithm for the DAP is presented. This algorithm iteratively solves a deterministic user equilibrium model for a given O–D matrix and a DAP restricted to the previously generated paths, whose solution generates a new O–D trip matrix estimation. The restricted DAP is formulated via a single level optimization problem. The convergence on local minimum of the proposed algorithm requires only the continuity of the link travel cost functions and the gauges used in the definition of the DAP. 相似文献
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