Mixed-integer nonlinear optimization
Many optimal decision problems in scientific, engineering, and public sector applications
involve both discrete decisions and nonlinear system dynamics that affect the quality of the …
involve both discrete decisions and nonlinear system dynamics that affect the quality of the …
Hardness of SIS and LWE with small parameters
D Micciancio, C Peikert - Annual cryptology conference, 2013 - Springer
Abstract The Short Integer Solution (SIS) and Learning With Errors (LWE) problems are the
foundations for countless applications in lattice-based cryptography, and are provably as …
foundations for countless applications in lattice-based cryptography, and are provably as …
A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations
D Micciancio, P Voulgaris - Proceedings of the Forty-second ACM …, 2010 - dl.acm.org
We give deterministic~ O (22n+ o (n))-time algorithms to solve all the most important
computational problems on point lattices in NP, including the Shortest Vector Problem …
computational problems on point lattices in NP, including the Shortest Vector Problem …
The subspace flatness conjecture and faster integer programming
V Reis, T Rothvoss - 2023 IEEE 64th Annual Symposium on …, 2023 - ieeexplore.ieee.org
In a seminal paper, Kannan and Lovász (1988) considered a quantity KL(Λ,K) which
denotes the best volume-based lower bound on the covering radius μ(Λ,K) of a convex body …
denotes the best volume-based lower bound on the covering radius μ(Λ,K) of a convex body …
[图书][B] Algebraic and geometric ideas in the theory of discrete optimization
It is undeniable that geometric ideas have been very important to the foundations of modern
discrete optimization. The influence that geometric algorithms have in optimization was …
discrete optimization. The influence that geometric algorithms have in optimization was …
Algorithms for the shortest and closest lattice vector problems
G Hanrot, X Pujol, D Stehlé - International Conference on Coding and …, 2011 - Springer
We present the state of the art solvers of the Shortest and Closest Lattice Vector Problems in
the Euclidean norm. We recall the three main families of algorithms for these problems …
the Euclidean norm. We recall the three main families of algorithms for these problems …
Solving the Closest Vector Problem in 2^ n Time--The Discrete Gaussian Strikes Again!
D Aggarwal, D Dadush… - 2015 IEEE 56th …, 2015 - ieeexplore.ieee.org
We give a 2 n+ o (n)-time and space randomized algorithm for solving the exact Closest
Vector Problem (CVP) on n-dimensional Euclidean lattices. This improves on the previous …
Vector Problem (CVP) on n-dimensional Euclidean lattices. This improves on the previous …
Combinatorial n-fold integer programming and applications
Many fundamental NP NP-hard problems can be formulated as integer linear programs
(ILPs). A famous algorithm by Lenstra solves ILPs in time that is exponential only in the …
(ILPs). A famous algorithm by Lenstra solves ILPs in time that is exponential only in the …
Slide reduction, revisited—filling the gaps in SVP approximation
We show how to generalize Gama and Nguyen's slide reduction algorithm STOC'08 for
solving the approximate Shortest Vector Problem over lattices (SVP) to allow for arbitrary …
solving the approximate Shortest Vector Problem over lattices (SVP) to allow for arbitrary …
[图书][B] Integer programming, lattice algorithms, and deterministic volume estimation
DN Dadush - 2012 - search.proquest.com
The main subject of this thesis is the development of new geometric tools and techniques for
solving classic problems within the geometry of numbers and convex geometry. At a high …
solving classic problems within the geometry of numbers and convex geometry. At a high …