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We address a class of integer optimization programs with a total variation-like regularizer and convex, separable constraints on a graph. Our approach makes use of the Graver basis, an optimality certificate for integer programs, which we…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
We describe an efficient implementation of a recent simplex-type algorithm for the exact solution of separated continuous linear programs, and compare it with linear programming approximation of these problems obtained via discretization of…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over…
In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…
Implementing graph algorithms efficiently in a rule-based language is challenging because graph pattern matching is expensive. In this paper, we present a number of linear-time implementations of graph algorithms in GP 2, an experimental…