Search

Events

VADOR / Events / AKOR Seminar, Fast continuous time methods for monotone equations, Radu Bot, University of Vienna
21. March 2024, 15:00 until 17:00
AKOR Seminar, Fast continuous time methods for monotone equations, Radu Bot, University of Vienna
Presentation
In this talk we discuss continuous in time dynamics for the problem of approaching the set of zeros of a single-valued monotone and continuous operator. Such problems are motivated by minimax convex-concave and, in particular, by convex optimization problems with linear constraints. The central role is played by a second-order dynamical system that combines a vanishing damping term with the time derivative of the operator along the trajectory, which can be seen as an analogous of the Hessian-driven damping in cases where the operator originates from a potential. We demonstrate that the norm of the operator along the trajectory and the restricted gap function exhibit fast vanishing behaviour, and that the trajectory converges weakly to a solution of the monotone equation. The implicit and explicit discrete time models, enhanced with Nesterov’s momentum and correcting terms, share the asymptotic features of the continuous dynamics. In the second part of the talk, we discuss the connection between the second-order dynamical system and a Tikhonov regularized first-order dynamical system, exhibiting fast convergence rates and strong convergence of the trajectory.

About Cookies

Our website uses cookies to ensure you get the best experience on our website, for analytical purposes, to provide social media features, and for targeted advertising. This it is necessary in order to pass information on to respective service providers. If you would like additional information about cookies on this website, please see our Data Protection Declaration.

  • These cookies are required to help our website run smoothly.

    Name Purpose Lifetime Type Provider
    wordpress_test_cookie Testing-Cookie to check whether cookies are allowed. 1 Year HTTP Homepage TUW
    PHPSESSID Used by WordPress to retain the state of your current user session for all page requests. Session HTTP Homepage TUW
    wordpress_logged_in_{hash} Used by Wordpress to keep users logged in. {hash} represents an unique user token. 1 Year HTTP Homepage TUW
    wp-settings-time-{id} Used to customize your view of admin interface, and possibly also the main site interface. 1 Year HTTP Homepage TUW
    wordpress_sec_{hash} This cookie is used to store your authentication details. Its use is limited to the admin console area. {hash} represents an unique user token. 1 Year HTTP Homepage TUW
    wp-settings-{id} Used to customize your view of admin interface, and possibly also the main site interface. 1 Year HTTP Homepage TUW
    wp-wpml_current_language Stores the current language. This cookie is enabled by default on sites that use the Language filtering for AJAX operations feature. 1 Day HTTP Homepage TUW
    wp-wpml_current_admin_language_{hash} Stores the current WordPress administration area language. {hash} represents an unique user token. 1 Day HTTP Homepage TUW
    CookieConsent_b92907 Saves your settings for the use of cookies on this website. 1 Year HTML Homepage TUW

  • These cookies help us to continuously improve our services and adapt our website to your needs. We statistically evaluate the pseudonymized data collected from our website.

    Name Purpose Lifetime Type Provider
    _pk_id.136.56ce Used to store a few details about the user such as the unique visitor ID. 13 months HTML Matomo TUW
    _pk_ref Is used to store the information of the users home website. 6 months HTML Matomo TUW
    _pk_ses.136.56ce Is needed to store temporary data of the visit. 30 minutes HTML Matomo TUW