We consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that defines the convex hull of the integer points in K that are not lexicographically smaller than x. The family of … Read more
In the setting of a Euclidean Jordan algebra V with symmetric cone V_+, corresponding to a linear transformation M, a `weight vector’ w in V_+, and a q in V, we consider the weighted linear complementarity problem wLCP(M,w,q) and (when w is in the interior of V_+) the interior point system IPS(M,w,q). When M is … Read more
We present an algorithm for finding the complete Pareto frontier of biobjective integer programming problems. The method is based on the solution of a finite number of integer programs. The feasible sets of the integer programs are built from the original feasible set, by adding cuts that separate efficient solutions. Providing the existence of an … Read more
We study a robust monopoly pricing problem with a minimax regret objective, where a seller endeavors to sell multiple goods to a single buyer, only knowing that the buyer’s values for the goods range over a rectangular uncertainty set. We interpret this pricing problem as a zero-sum game between the seller, who chooses a selling … Read more
In the last decades, research on emergency traffic management has received high attention from the operations research community and many pioneer researchers have established it as one of the most fertile research areas. We consider the computationally hard flows over time problems from wider perspective including flow/time dependent attributes (dynamic flows), a possibility of flows … Read more
In the arXiv paper [arXiv:1712.07761] from December 2017 we presented a convergent direct transcription method for optimal control problems. In the present paper we present a significantly generalized convergence theory in succinct form. Therein, we replace strong assumptions that we had formerly made on local uniqueness of the solution, and on differentiability of a particular … Read more
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