the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...

The problem of finding the minimum cost multi-commodity flow in an undirected and complete network is studied when the link costs are piecewise linear and convex. The arc-path model and overflow model are presented to formulate the problem. The results suggest that the new overflow model outperforms the classical arc-path model for this problem. The classical revised simplex, Frank and Wolf and...

3 Non-linear Objective functions 4 3.1 Production problem with set-up costs . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Piecewise linear cost function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.3 Piecewise linear convex cost function . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Disjunctive constraints . . . . . . . . . . . . . . . . . . . . . ...

We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.

We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on d...

We present an approximation method for inventory management under multiple suppliers and stochastic lead times. The method is based on parametric dynamic programming using convex piecewise linear approximations of the differential cost function in approximate relative value iteration steps and works for a range of stochastic control problems with linear dynamics and convex piecewise linear imme...