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We introduce a recent symplectic integration scheme derived for solving physically motivated systems with non-separable Hamiltonians. We show its relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an alternative to…

Machine Learning · Statistics 2019-10-15 Adam D. Cobb , Atılım Güneş Baydin , Andrew Markham , Stephen J. Roberts

This paper introduces a general class of Replicator-Mutator equations on a multi-dimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fockker-Planck-Kolmogorov…

Analysis of PDEs · Mathematics 2020-03-16 Lijun Bo , Huafu Liao

Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding constraints in SMT theory solvers is highly relevant. We propose…

Logic in Computer Science · Computer Science 2018-04-30 Pascal Fontaine , Mizuhito Ogawa , Thomas Sturm , Xuan Tung Vu

Decision procedures for SMT problems based on the theory of bit-vectors are a fundamental component in state-of-the-art software and hardware verifiers. While very efficient in general, certain SMT instances are still challenging for…

Logic in Computer Science · Computer Science 2020-08-25 Samuel Teuber , Marko Kleine Büning , Carsten Sinz

In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…

Numerical Analysis · Mathematics 2012-05-09 S. M. Abrarov , B. M. Quine

This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…

Numerical Analysis · Mathematics 2014-07-08 Sivaram Ambikasaran , Eric Darve

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable…

Optimization and Control · Mathematics 2017-03-27 Songtao Lu , Mingyi Hong , Zhengdao Wang

Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…

Numerical Analysis · Computer Science 2013-11-19 Srikrishna Sridhar , Victor Bittorf , Ji Liu , Ce Zhang , Christopher Ré , Stephen J. Wright

Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…

Logic in Computer Science · Computer Science 2024-08-27 Jian Cao , Liyong Lin , Lele Li

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…

Optimization and Control · Mathematics 2019-05-02 Evgeny Shindin , Gideon Weiss

The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…

Numerical Analysis · Mathematics 2017-06-28 Manas Rachh , Andreas Klöckner , Michael O'Neil

Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…

Numerical Analysis · Mathematics 2024-07-17 Rafał Perczyński , Antoni Augustynowicz

In this paper we propose a novel approach for checking satisfiability of non-linear constraints over the reals, called ksmt. The procedure is based on conflict resolution in CDCL style calculus, using a composition of symbolical and…

Logic in Computer Science · Computer Science 2019-07-08 Franz Brauße , Konstantin Korovin , Margarita Korovina , Norbert Th. Müller

We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…

Optimization and Control · Mathematics 2019-12-02 Mattias Fält , Pontus Giselsson

While teaching a course on integral equations, I noticed that a straightforward combination of Neumann series and Fourier series for the resolvent (or the solution) of an integral equation has good approximation qualities. This short…

Classical Analysis and ODEs · Mathematics 2021-01-05 Raimundas Vidunas

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

Optimization and Control · Mathematics 2023-07-13 Maria-Luiza Vladarean , Nikita Doikov , Martin Jaggi , Nicolas Flammarion

We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…

Optimization and Control · Mathematics 2022-03-25 Nathan Adelgren

SMT solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing…

Logic in Computer Science · Computer Science 2017-06-02 Andrew Reynolds , Cesare Tinelli , Clark Barrett

Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…

Logic in Computer Science · Computer Science 2025-08-13 Mudathir Mohamed , Nick Feng , Andrew Reynolds , Cesare Tinelli , Clark Barrett , Marsha Chechik

We consider the homogenized linear feasibility problem, to find an $x$ on the unit sphere, satisfying $n$ line ar inequalities $a_i^Tx\ge 0$. To solve this problem we consider the centers of the insphere of spherical simpl ices, whose…

Optimization and Control · Mathematics 2007-05-23 Ulrich Betke