The classic version of the Inventory Routing Problem considers a system with one supplier that manages the stock level of a set of customers. The supplier defines when and how much products to supply and how to combine customers in routes while minimizing storage and transportation costs. We present a new version of this problem … Read more
Motivated by Chubanov’s projection-based method for linear feasibility problems [Chubanov2015], a projection and rescaling algorithm for the conic feasibility problem \[ find \; x\in L\bigcap \Omega \] is proposed in [Pena2016], where $L$ and $\Omega$ are respectively a linear subspace and the interior of a symmetric cone in a finitely dimensional vector space $V$. When … Read more
State-of-the-art solvers for mixed integer programs (MIP) govern a variety of algorithmic components. Ideally, the solver adaptively learns to concentrate its computational budget on those components that perform well on a particular problem, especially if they are time consuming. We focus on three such algorithms, namely the classes of large neighborhood search and diving heuristics … Read more
Chvatal (1980) has given a simple example of a knapsack problem for which a branch-and-bound algorithm using domination and linear relaxations to eliminate subproblems will use an exponential number of steps in the best case. In this short note it is shown that Chvatals result remains true when the LP relaxation is replaced with a … Read more
Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthormalization methods are derived, the necessary quantities occurring in the theoretical bounds estimated and new practical algorithms derived. Numerical experiments suggest that the new methods have significant … Read more
Two-trust-region subproblem (TTRS), which is the minimization of a general quadratic function over the intersection of two full-dimensional ellipsoids, has been the subject of several recent research. In this paper, to solve TTRS, a hybrid of efficient algorithms for finding global and local-nonglobal minimizers of trust-region subproblem and the alternating direction method of multipliers (ADMM) … Read more
Critical infrastructure systems in cities are becoming increasingly interdependent, therefore exacerbating the impacts of disruptive events through cascading failures, hindered asset repairs and network congestion. Current resilience assessment methods fall short of fully capturing such interdependency effects as they tend to model asset reliability and network flows separately and often rely on static flow assignment … Read more
In this paper, scalarizing functions defined with the help of the Hiriart-Urruty signed distance are used to characterize set order relations and weak optimal solutions in set optimization studied with Kuroiwa’s set approach and to introduce a new concept of slope for a set-valued map. It turns out that this slope possesses most properties of … Read more
The Douglas-Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In this paper we propose a structural generalization that allows to use r-sets-DR operators in a cyclic fashion. We prove convergence and present numerical illustrations of the potential advantage of such … Read more
In this paper, we study characterizations of differentiability for real-valued functions based on generalized differentiation. These characterizations provide the mathematical foundation for Nesterov’s smoothing techniques in infinite dimensions. As an application, we provide a simple approach to image reconstructions based on Nesterov’s smoothing techniques and DC programming that involves the $\ell_1-\ell_2$ regularization. Article Download View … Read more