Seminar: Lucas Slot (CWI) + Juan José Maulén (Groningen), 2 PhD talks

Speaker: Lucas Slot (CWI Amsterdam) + Juan José Maulén (RU Groningen)

Title:

Lucas Slot: Degree bounds for positivity certificates and the polynomial kernel method 

Juan José Maulén: Acceleration of fixed point algorithms via inertia

Zoom link: 

https://cwi-nl.zoom.us/j/84909645595?pwd=b1M4QnNKVzNMdmNSVFNaZUJmR1kvUT09
(Meeting ID: 849 0964 5595, Passcode: 772448)

Abstract of "Degree bounds for positivity certificates and the polynomial kernel method" (Lucas Slot):

The classical Positvestellensaetze of Putinar and Schmuedgen state that the positivity of a polynomial f over a (compact) semialgebraic set S can be verified by expanding f as a conic combination of the polynomials that define S, using sums of squares of polynomials as coefficients. Recently, there has been an interest in proving bounds on the largest degree of the sum-of-squares coefficients involved in this expansion. Such bounds have direct implications for the convergence rate of Lasserre-type hierarchies for polynomial optimization. We present the polynomial kernel method for proving degree bounds on special sets S, which was first used in the case of the hypersphere by Fang and Fawzi.
We apply the PKM to additional sets, including the binary hypercube {-1, 1}^n, the unit box [-1, 1]^n and the unit ball.

This is based on joint work with Monique Laurent.
Arxiv link: https://arxiv.org/abs/2011.04027

Video of the talk of Lucas Slot:

Slides of the talk of Lucas Slot:  

Slides

 

Abstract of "Acceleration of fixed point algorithms via inertia" (Juan José Maulén):

In this talk, we will use the results about the convergence of inertial optimization algorithms, defined as fixed point iterations from a family of cocoercive operators. This result implies that exists inertial versions of the Primal-dual splitting algorithm proposed by Briceño and Roldan on 2019, and for the three-operator splitting scheme proposed by Davis and Yin on 2015. Both algorithms fit on the framework of optimization algorithms defined by cocoercive operators. The inertial versions obtained are tested in several numerical experiments, where  better performance with respect to the original algorithms can be observed.

Video of the talk of Juan José Maulén:

Slides of the talk of Juan José Maulén: 

Slides