Lagrangean Duality Applied on Vehicle Routing with Time Windows

This paper presents the results of the application of a non-differentiable optimization method in connection with the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW is an extension of the Vehicle Routing Problem. In the VRPTW the service at each customer must start within an associated time window. The Shortest Path decomposition of the … Read more

Polynomial interior point cutting plane methods

Polynomial cutting plane methods based on the logarithmic barrier function and on the volumetric center are surveyed. These algorithms construct a linear programming relaxation of the feasible region, find an appropriate approximate center of the region, and call a separation oracle at this approximate center to determine whether additional constraints should be added to the … Read more

Multiple Cuts with a Homogeneous Analytic Center Cutting Plane Method

This paper analyzes the introduction of multiple central cuts in a conic formulation of the analytic center cutting plane method (in short ACCPM). This work extends earlier work on the homogeneous ACCPM, and parallels the analysis of the multiple cut process in the standard ACCPM. The main issue is the calculation of a direction that … Read more

A Linear Programming Approach to Semidefinite Programming Problems

Until recently, the study of interior point methods has dominated algorithmic research in semidefinite programming (SDP). From a theoretical point of view, these interior point methods offer everything one can hope for; they apply to all SDP’s, exploit second order information and offer polynomial time complexity. Still for practical applications with many constraints $k$, the … Read more

Lagrangian relaxation

Lagrangian relaxation is a tool to find upper bounds on a given (arbitrary) maximization problem. Sometimes, the bound is exact and an optimal solution is found. Our aim in this paper is to review this technique, the theory behind it, its numerical aspects, its relation with other techniques such as column generation. Citation in: Computational … Read more

Facets of the Complementarity Knapsack Polytope

We present a polyhedral study of the complementarity knapsack problem, in which no auxiliary binary variables are introduced, but rather the inequalities are derived in the space of the continuous variables. Citation School of Industrial and Systems Engineering, GA Tech, under review Article Download View Facets of the Complementarity Knapsack Polytope