Application of Global Line-Search in the Optimization of Networks
An application of Global Line-Search (GLS) to the optimization of networks is considered in this chapter. Advantages and disadvantages are discussed. It is shown that GLS provides the global minimum after a finite number of steps in two cases of piecewise linear cost functions of arcs. The first case is, where all cost functions are convex. The second case is, where all costs are equal to zero at zero flow, and equal to some constant at non-zero flow. In other cases the global line-search approaches the global minimum with a small average error. Therefore this algorithm is regarded as a good heuristics.
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