Publications related to Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma

On the boundedness of n-folds with κ(X) = n - 1

In this note, we study certain sufficient conditions for a set of minimal klt pairs ( X, triangle) with kappa ( X, triangle) = dim( X ) - 1 to be bounded. ...

European Mathematical Soc-Ems2024

Non-normal forms

Yves-Marie François Ducimetière

In this thesis, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing, or to an initial condition. This approach reconciles the non-mo ...

EPFL2024

Improving SAM Requires Rethinking its Optimization Formulation

Volkan Cevher, Kimon Antonakopoulos, Thomas Michaelsen Pethick, Wanyun Xie, Fabian Ricardo Latorre Gomez

This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. We argue that SAM shou ...

2024

Results on Sparse Integer Programming and Geometric Independent Sets

Jana Tabea Cslovjecsek

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n.Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed p ...

EPFL2023

Removing Algorithmic Discrimination (With Minimal Individual Error)

Rachid Guerraoui, El Mahdi El Mhamdi, Alexandre David Olivier Maurer, Le Nguyen Hoang

We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analy ...

2022

Removing algorithmic discrimination (with minimal individual error)

Rachid Guerraoui, El Mahdi El Mhamdi, Alexandre David Olivier Maurer, Le Nguyen Hoang

We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analy ...

ELSEVIER2022

Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity

Friedrich Eisenbrand, Moritz Andreas Venzin, Jana Tabea Cslovjecsek

We consider the problem of solving integer programs of the form min {c^⊺ x : Ax = b, x ∈ ℤ_{⩾ 0}}, where A is a multistage stochastic matrix in the following sense: the primal treedepth of A is bounded by a parameter d, which means that the columns of A ca ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Complexity of linear relaxations in integer programming

Matthias Schymura

For a set X of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with X is called the relaxation complexity rc(X). This parameter was introduced by Kaibel & Weltge (2015) and captures the ...

2020

Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma

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On the boundedness of n-folds with κ(X) = n - 1

Non-normal forms

Improving SAM Requires Rethinking its Optimization Formulation

Results on Sparse Integer Programming and Geometric Independent Sets

Removing Algorithmic Discrimination (With Minimal Individual Error)

Removing algorithmic discrimination (with minimal individual error)

Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

New Results in Integer and Lattice Programming

Complexity of linear relaxations in integer programming

Non-normal forms

Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity

On the boundedness of n-folds with κ(X) = n - 1

Results on Sparse Integer Programming and Geometric Independent Sets

Improving SAM Requires Rethinking its Optimization Formulation

Removing algorithmic discrimination (with minimal individual error)

Complexity of linear relaxations in integer programming

Removing Algorithmic Discrimination (With Minimal Individual Error)

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

New Results in Integer and Lattice Programming