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We study the integrality gap of convex mixed-integer programs, that is, the difference between the optimal value of such a problem and the optimal value of its continuous relaxation. We study classes of convex sets whose associated…

Optimization and Control · Mathematics 2026-04-20 Burak Kocuk , Diego Moran Ramirez

A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…

Optimization and Control · Mathematics 2025-10-24 Tobia Marcucci

Given an undirected graph, the k-vertex cut problem (k-VCP) asks for a minimum-cost set of vertices whose removal yields at least k connected components in the resulting graph. The k-VCP is an important problem in network optimization, with…

Optimization and Control · Mathematics 2026-02-06 Fabio Ciccarelli , Fabio Furini , Christopher Hojny , Marco Lübbecke

We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this…

Discrete Mathematics · Computer Science 2009-03-10 Manoel Campelo , Ricardo C. Correa

We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.

Combinatorics · Mathematics 2007-05-23 Nikolai Yu. Zolotykh

A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…

Optimization and Control · Mathematics 2023-04-25 Niklas Hey , Andreas Löhne

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…

Optimization and Control · Mathematics 2017-01-03 Jesús A. De Loera , Raymond Hemmecke , Matthias Köppe , Robert Weismantel

This letter concerns optimal power transmission line inspection formulated as a proposed generalization of the traveling salesman problem for a multi-route one-depot scenario. The problem is formulated for an inspection vehicle with a…

Robotics · Computer Science 2023-02-03 František Nekovář , Jan Faigl , Martin Saska

Due to the limited connectivity of gate model quantum devices, logical quantum circuits must be compiled to target hardware before they can be executed. Often, this process involves the insertion of SWAP gates into the logical circuit,…

Quantum Physics · Physics 2023-06-16 Kyle E. C. Booth

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Data Structures and Algorithms · Computer Science 2020-03-19 Agniva Chowdhury , Palma London , Haim Avron , Petros Drineas

We consider convex-concave saddle point problems, and more generally convex optimization problems we refer to as $\textit{saddle problems}$, which include the partial supremum or infimum of convex-concave saddle functions. Saddle problems…

Optimization and Control · Mathematics 2024-01-11 Philipp Schiele , Eric Luxenberg , Stephen Boyd

We introduce an extension of decision problems called resiliency problems. In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation has been applied to it. To tackle…

Data Structures and Algorithms · Computer Science 2018-05-04 Jason Crampton , Gregory Gutin , Martin Koutecký , Rémi Watrigant

An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…

Optimization and Control · Mathematics 2026-01-22 Jamie Fravel , Robert Hildebrand

In the Model-Driven Software Engineering (MDSE) community, the combination of techniques operating on graph-based models (e.g., Pattern Matching (PM) and Graph Transformation (GT)) and Integer Linear Programming (ILP) is a common…

Software Engineering · Computer Science 2024-05-16 Sebastian Ehmes , Maximilian Kratz , Andy Schürr

We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…

Optimization and Control · Mathematics 2019-07-09 Vincent Guigues

The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…

Data Structures and Algorithms · Computer Science 2020-09-22 Mark Sh. Levin

We consider the minimum weight and smallest weight minimum-size dominating set problems in vertex-weighted graphs and networks. The latter problem is a two-objective optimization problem, which is different from the classic minimum weight…

Combinatorics · Mathematics 2024-01-23 Lukas Dijkstra , Andrei Gagarin , Vadim Zverovich

In this paper, we propose novel mixed-integer linear programming (MIP) formulations to model decision problems posed as influence diagrams. We also present a novel heuristic that can be employed to warm start the MIP solver, as well as…

Optimization and Control · Mathematics 2026-01-21 Helmi Hankimaa , Olli Herrala , Fabricio Oliveira , Jaan Tollander de Balsch

This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…

Optimization and Control · Mathematics 2011-08-01 Tran Dinh Quoc , Moritz Diehl

The partition of a problem into smaller sub-problems satisfying certain properties is often a key ingredient in the design of divide-and-conquer algorithms. For questions related to location, the partition problem can be modeled, in…

Computational Geometry · Computer Science 2020-12-08 Allan Sapucaia , Pedro J. de Rezende , Cid C. de Souza