8 citations · 17 across the 17 of their papers we have counts for
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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…