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03/26/2023
Convergence rates for sums-of-squares hierarchies with correlative sparsity
This work derives upper bounds on the convergence rate of the moment-sum...
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02/04/2023
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
Pourchet proved in 1971 that every nonnegative univariate polynomial wit...
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09/13/2022
Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant
We consider polynomial optimization problems (POP) on a semialgebraic se...
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08/23/2022
Sparse Polynomial Optimization: Theory and Practice
The problem of minimizing a polynomial over a set of polynomial inequali...
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02/14/2022
Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients
Certifying the positivity of trigonometric polynomials is of first impor...
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02/09/2022
Stability Analysis of Recurrent Neural Networks by IQC with Copositive Mutipliers
This paper is concerned with the stability analysis of the recurrent neu...
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07/25/2021
Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients
Assessing non-negativity of multivariate polynomials over the reals, thr...
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03/01/2021
TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization
The Julia library TSSOS aims at helping polynomial optimizers to solve l...
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12/14/2020
SONC Optimization and Exact Nonnegativity Certificates via Second-Order Cone Programming
The second-order cone (SOC) is a class of simple convex cones and optimi...
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06/17/2020
Computer-assisted proofs for Lyapunov stability via Sums of Squares certificates and Constructive Analysis
We provide a computer-assisted approach to ensure that a given continuou...
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05/06/2020
CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solv...
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02/10/2020
Polynomial Optimization for Bounding Lipschitz Constants of Deep Networks
The Lipschitz constant of a network plays an important role in many appl...
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02/06/2019
Exact Optimization via Sums of Nonnegative Circuits and Sums of AM/GM Exponentials
We provide two hybrid numeric-symbolic optimization algorithms, computin...
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11/25/2018
On Exact Reznick, Hilbert-Artin and Putinar's Representations
We consider the problem of finding exact sums of squares (SOS) decomposi...
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11/25/2018
On Exact Polya, Hilbert-Artin and Putinar's Representations
We consider the problem of finding exact sums of squares (SOS) decomposi...
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05/06/2018
RealCertify: a Maple package for certifying non-negativity
Let Q (resp. R) be the field of rational (resp. real) numbers and X = (X...
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02/28/2018
On Exact Polya and Putinar's Representations
We consider the problem of finding exact sums of squares (SOS) decomposi...
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02/12/2018
Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations
Floating point error is a drawback of embedded systems implementation th...
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06/13/2017