Local optimality conditions for multicommodity flow problems with separable piecewise convex costs

摘要

We consider here a multicommodity flow network optimization problem with non-convex but piecewise convex arc cost functions. We derive complete optimality conditions for local minima based on negative-cost cycles associated with each commodity. These conditions do not extend to the convex non-smooth case. (c) 2006 Elsevier B.V. All rights reserved.