Strong Convergence of Inertial Algorithms via Tikhonov Regularization

Explore the application of Tikhonov regularization in optimization algorithms during this 24-minute conference talk from the "One World Optimization Seminar in Vienna" workshop at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the benefits of introducing Tikhonov regularization terms in minimization problem algorithms, allowing for pre-selection of equilibrium points and strong topology convergence. Examine two inertial algorithms with Tikhonov regularization: a proximal algorithm for non-smooth objective functions and a Nesterov-type algorithm for differentiable objective functions. Discover the relationship between extrapolation coefficients and Tikhonov regularization parameters, and learn about parameter settings that ensure strong convergence to the minimum norm solution while maintaining fast convergence for objective function values. Investigate an inertial gradient-type algorithm with dual Tikhonov regularization terms, exploring its strong convergence properties and Nesterov-type rates. Understand the crucial role of both regularization terms in achieving convergence to the minimal norm solution.