8 citations · 17 across the 17 of their papers we have counts for
20 papers
Quantum speed-ups for solving semidefinite relaxations of polynomial optimization
Daniel Stilck França, Ngoc Hoang Anh Mai
We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let be real polynomials in variables and the…
Sums of squares representations on singular loci
Ngoc Hoang Anh Mai, Victor Magron
The problem of characterizing a real polynomial as a sum of squares of polynomials on a real algebraic variety dates back to the pioneering work of Hilbert in [Mathematisch…
A Nichtnegativstellensatz on singular varieties under the denseness of regular loci
Ngoc Hoang Anh Mai
Let be a real algebraic variety with singularities and be a real polynomial non-negative on . Assume that the regular locus of is dense in by the usual topology.…
Semi-algebraic description of the closure of the image of a semi-algebraic set under a polynomial
Ngoc Hoang Anh Mai
Given a polynomial and a semi-algebraic set , we provide a symbolic algorithm to find the equations and inequalities defining a semi-algebraic set which is identical to…
Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre +1
We consider polynomial optimization problems (POP) on a semialgebraic set contained in the nonnegative orthant (every POP on a compact set can be put in this format by a simple tra…
A symbolic algorithm for exact polynomial optimization strengthened with Fritz John conditions
Ngoc Hoang Anh Mai
Consider a polynomial optimization problem. Adding polynomial equations generated by the Fritz John conditions to the constraint set does not change the optimal value. As proved in…
Complexity for exact polynomial optimization strengthened with Fritz John conditions
Ngoc Hoang Anh Mai
Let be polynomials of degree at most with real coefficients in a vector of variables . Assume that is non-negative on a basic semi-alge…
On the exactness for polynomial optimization strengthened with Fritz John conditions
Ngoc Hoang Anh Mai
We utilize the same technique as in [arXiv:2205.04254 (2022)] to provide some representations of polynomials non-negative on a basic semi-algebraic set, defined by polynomial inequ…
Exact polynomial optimization strengthened with Fritz John conditions
Ngoc Hoang Anh Mai
Let be polynomials with real coefficients in a vector of variables . Denote by the diagonal matrix with coefficients $g=(g_1,\…
Tractable semidefinite bounds of positive maximal singular values
Victor Magron, Ngoc Hoang Anh Mai, Yoshio Ebihara +1
We focus on computing certified upper bounds for the positive maximal singular value (PMSV) of a given matrix. The PMSV problem boils down to maximizing a quadratic polynomial on t…
Stability Analysis of Recurrent Neural Networks by IQC with Copositive Mutipliers
Yoshio Ebihara, Hayato Waki, Victor Magron +3
This paper is concerned with the stability analysis of the recurrent neural networks (RNNs) by means of the integral quadratic constraint (IQC) framework. The rectified linear unit…
On the complexity of Putinar-Vasilescu's Positivstellensatz
Ngoc Hoang Anh Mai, Victor Magron
We provide a new degree bound on the weighted sum-of-squares (SOS) polynomials for Putinar-Vasilescu's Positivstellensatz. This leads to another Positivstellensatz saying that if $…
The Constant Trace Property in Noncommutative Optimization
Ngoc Hoang Anh Mai, Abhishek Bhardwaj, Victor Magron
In this article, we show that each semidefinite relaxation of a ball-constrained noncommutative polynomial optimization problem can be cast as a semidefinite program with a constan…
Comparing different subgradient methods for solving convex optimization problems with functional constraints
Thi Lan Dinh, Ngoc Hoang Anh Mai
We consider the problem of minimizing a convex, nonsmooth function subject to a closed convex constraint domain. The methods that we propose are reforms of subgradient methods base…
Exploiting constant trace property in large-scale polynomial optimization
Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron +1
We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matri…
Induced Norm Analysis of Discrete-Time LTI Systems for Nonnegative Input Signals and Its Application to Stability Analysis of Recurrent Neural Networks
Yoshio Ebihara, Hayato Waki, Victor Magron +3
In this paper, we focus on the "positive" induced norm of discrete-time linear time-invariant systems where the input signals are restricted to be nonnegative. To cope with t…
A hierarchy of spectral relaxations for polynomial optimization
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre
We show that (i) any constrained polynomial optimization problem (POP) has an equivalent formulation on a variety contained in an Euclidean sphere and (ii) the resulting semidefini…
CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization
Jie Wang, Victor Magron, Jean B. Lasserre +1
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlativ…
A sparse version of Reznick's Positivstellensatz
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre
If is a positive definite form, Reznick's Positivstellensatz [Mathematische Zeitschrift. 220 (1995), pp. 75--97] states that there exists such that ${\| x \|^{…
Positivity certificates and polynomial optimization on non-compact semialgebraic sets
Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron
In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu [Comptes Rendus de l'Académie des…