We prove a representation theorem of projections of sets of integer points by an integer matrix W . Our result can be seen as a polyhedral analogue of several classical and recent results related to the Frobenius problem. Our result is motivated by a large class of non-linear integer optimization problems in variable dimension. Concretely, we aim to optimize f(Wx) over a set F = P ∩ Z, where f ...

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.

Water is a basic part of our daily lives, as such effective water supply paramount importance. Thus, result the rise in population size and shortage there need for proper, suitable optimal utilization resources to efficiently be distributed among populace. The proper allocation distribution field network planning modelled through mathematical parameters objective system. This approach requires ...

We present a Mixed Integer Linear Programming (MILP) approach in order to model the non-linear problem of minimizing tire noise function. In recent work, we proposed an exact solution for Tire Noise Optimization Problem, dealing with APproximation (TNOP-AP). Here study original modeling EXact- or real-noise (TNOP-EX) and propose new scheme obtain TNOP-EX. Relying on TNOP-AP, use Branch&Cut ...