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math.OC2021
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 $…
math.OC2021
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…
math.OC2021
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…