This paper gives a unified and succinct approach to the $O(1/\sqrt{k}), O(1/k),$ and $O(1/k^2)$ convergence rates of the subgradient, gradient, and accelerated gradient methods for unconstrained convex minimization. In the three cases the proof of convergence follows from a generic bound defined by the convex conjugate of the objective function. CitationWorking Paper, Carnegie Mellon UniversityArticleDownload … Read more
In this paper, we propose a model for the generation and transmission network expansion planning problem that includes decisions related to substations’ locations and sizes. In power system expansion planning problems, locations of generation units and/or transmission lines are determined. However, substation location decisions are not explicitly studied. Nevertheless, including the decisions of substations’ locations … Read more
We address the multi container loading problem of a company that has to serve its customers by first putting the products on pallets and then loading the pallets into trucks. We approach the problem by developing and solving integer linear models. To be useful in practice, our models consider three types of constraints: geometric constraints, … Read more
Same-day delivery of online orders is becoming an indispensable service for large retailers. We explore an environment in which in-store customers supplement company drivers and can take on the task of delivering online orders on their way home. Because online orders as well as in-store customers willing to make deliveries arrive throughout the day, it … Read more
This paper describes an implementation of the L-BFGS method designed to deal with two adversarial situations. The first occurs in distributed computing environments where some of the computational nodes devoted to the evaluation of the function and gradient are unable to return results on time. A similar challenge occurs in a multi-batch approach in which … Read more
This paper analyzes sequences generated by infeasible interior point methods. In convex and non-convex settings, we prove that moving the primal feasibility at the same rate as complementarity will ensure that the Lagrange multiplier sequence will remain bounded, provided the limit point of the primal sequence has a Lagrange multiplier, without constraint qualification assumptions. We … Read more
Multistage stochastic programming problems are an important class of optimisation problems, especially in energy planning and scheduling. These problems and their solution methods have been of particular interest to researchers in stochastic programming recently. Because of the large scenario trees that these problems induce, current solution methods require random sampling of the tree in order … Read more
Let a (generalized) chessboard in two or three dimensions be given. A closed knight’s tour is defined as a Hamiltonian cycle over all cells of the chessboard where all moves are knight’s moves, i.,e. have length 5^0.5. It is well-characterized for which chessboard sizes it is not possible to construct a closed knight’s tour. On … Read more
We study the traveling salesperson problem with forbidden neighborhoods (TSPFN) on regular three-dimensional grids. The TSPFN asks for a shortest tour over all grid points such that successive points along a tour have at least some given distance. We present optimal solutions and explicit construction schemes for the Euclidean TSP and the TSPFN where edges … Read more
We study a class of monotone inclusions called “self-concordant inclusion” which covers three fundamental convex optimization formulations as special cases. We develop a new generalized Newton-type framework to solve this inclusion. Our framework subsumes three schemes: full-step, damped-step and path-following methods as specific instances, while allows one to use inexact computation to form generalized Newton … Read more