TY - JOUR
T1 - An ε-relaxation method for separable convex cost generalized network flow problems
AU - Tseng, Paul
AU - Bertsekas, Dimitri P.
PY - 2000/6
Y1 - 2000/6
N2 - We generalize the ε-relaxation method of [14] for the single commodity, linear or separable convex cost network flow problem to network flow problems with positive gains. The method maintains ε-complementary slackness at all iterations and adjusts the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves either a price change on a node or a flow change along an arc or a flow change along a simple cycle. Complexity bounds for the method are derived. For one implementation employing ε-scaling, the bound is polynomial in the number of nodes N, the number of arcs A, a certain constant Γ depending on the arc gains, and ln(ε0/ε̄), where ε0 and ε̄ denote, respectively, the initial and the final tolerance ε.
AB - We generalize the ε-relaxation method of [14] for the single commodity, linear or separable convex cost network flow problem to network flow problems with positive gains. The method maintains ε-complementary slackness at all iterations and adjusts the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves either a price change on a node or a flow change along an arc or a flow change along a simple cycle. Complexity bounds for the method are derived. For one implementation employing ε-scaling, the bound is polynomial in the number of nodes N, the number of arcs A, a certain constant Γ depending on the arc gains, and ln(ε0/ε̄), where ε0 and ε̄ denote, respectively, the initial and the final tolerance ε.
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U2 - 10.1007/PL00011379
DO - 10.1007/PL00011379
M3 - Article
AN - SCOPUS:0007638942
SN - 0025-5610
VL - 88
SP - 85
EP - 104
JO - Mathematical Programming, Series B
JF - Mathematical Programming, Series B
IS - 1
ER -