Dantzig-Wolfe decomposition (DWD) is a classical algorithm for solving large-scale linear programs whose constraint matrix involves a set of independent blocks coupled with a set of linking rows. The algorithm decomposes such a model into a master problem and a set of independent subproblems that can be solved in a distributed manner. In a typical … Read more
We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the primal oracle complexity, while it has competitive dual oracle complexity. In addition, we consider the situation where the primal-dual coupling term has … Read more
We give a characterization of the Hoffman constant of a system of linear constraints in $\R^n$ relative to a reference polyhedron $R\subseteq\R^n$. The reference polyhedron $R$ represents constraints that are easy to satisfy such as box constraints. In the special case $R = \R^n$, we obtain a novel characterization of the classical Hoffman constant. More … Read more
We address a stochastic variant of the Vehicle Routing Problem with Roaming Delivery Locations. In this model, direct-to-consumer deliveries can be made in the trunk of the customer’s car, while the vehicle is parked at a location along the customer’s itinerary. The stochasticity arises from the uncertainty in travel times and the problem is formulated … Read more
The World Food Programme (WFP) is the largest humanitarian agency fighting hunger worldwide, reaching around 90 million people with food assistance in 80 countries each year. To deal with the operational complexities inherent in its mandate, WFP has been developing tools to assist its decision makers with integrating supply chain decisions across departments and functional … Read more
This paper presents a Python package to solve multi-stage stochastic linear programs (MSLP) and multi-stage stochastic integer programs (MSIP). Algorithms based on an extensive formulation and Stochastic Dual Dynamic (Integer) Programming (SDDP/SDDiP) method are implemented. The package is synthetically friendly and has a number of features which are not available in the competing software packages. … Read more
We study a variant of the multi-period vehicle routing problem, in which a service provider offers a discount to customer in exchange for delivery flexibility. We establish theoretical properties and empirical insights regarding the intricate and complex relation between the benefit from additional delivery flexibility, the discounts offered to customers to gain additional delivery flexibility, … Read more
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost to go functions. An example of such a class of cuts are those derived using … Read more
Diverse forms of nonlinear optimization problems can be recast to the special form of second-order cone problems (SOCPs), permitting a wider variety of highly effective solvers to be applied. Popular solvers assume, however, that the necessary transformations to required canonical forms have already been identified and carried out. We describe a general approach to the … Read more
In this article, we consider the Krasnosel’ski\u{\i}-Mann iteration for approximating a fixed point of any given non-expansive operator in real Hilbert spaces, and we study an inertial version proposed by Maing\'{e} recently. As a result, we suggest new conditions on the inertial factors to ensure weak convergence. They are free of iterates and depend on … Read more