A branch-and-cut mixed integer programming system, called bc − opt, is described, incorporating most of the valid inequalities that have been used or suggested for such systems, namely lifted 0-1 knapsack inequalities, 0-1 gub knapsack and integer knapsack inequalities, flowcover and continuous knapsack inequalities, path inequalities for fixed charge network flow structure and Gomory mixed int...

This work pertains to the Knuth-Bendix (KB) algorithm which tries to find a complete set of reductions from a given set of equations. In the KB algorithm a term ordering is employed and it is required that every equation be orientable in the sense that the left-hand side be greater than the right. The KB algorithm halts if a nonorientable equation is produced. A generalization of the KB algorit...

The Brunn-Minkowski inequality theory plays an important role in a number of mathematical disciplines such as measure theory, crystallography, optimal control theory, functional analysis, and geometric convexity. It has many useful applications in combinatorics, stochastic geometry, and mathematical economics. In recent years, several authors including Ball [1, 2, 3], Bourgain and Lindenstrauss...

This paper considers 2D feedback systems modeled a by repetitive process where both the forward path and the feedback paths are nonlinear. Using a Lyapunov function approach, sufficient conditions for exponential stability are obtained and in the linear case the connection between exponential stability and the existing stability along the pass theory is established. The results are then extende...

In the traveling salesman path problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination visiting all cities exactly once. In this paper, we study polyhedral and combinatorial properties of a variant we call the traveling salesman walk problem, in which the object...

A caterpillar network (or graph) G is a tree with the property that removal of the leaf edges of G leaves one with a path. Here we focus on minimum weight spanning caterpillars (MSCs) where the vertices are points in the Euclidean plane and the costs of the path edges and the leaf edges are multiples of their corresponding Euclidean lengths. The flexibility in choosing the weight for path edges...

The Split Delivery Vehicle Routing Problem with Time Windows (SDVRPTW) is a notoriously hard combinatorial optimization problem. First, it is hard to find a useful compact Mixed-Integer Programming (MIP) formulation for the SDVRPTW. Standard modeling approach either suffer from inherent symmetries (MIPs with a vehicle index) or cannot exactly capture all aspects of feasibility. Due to the possi...