Related papers: Fast optimization via inertial dynamics with close…

In this work, we investigate a second-order dynamical system with Hessian-driven damping tailored for a class of nonconvex functions called strongly quasiconvex. Buil\-ding upon this continuous-time model, we derive two discrete-time…

Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…

In a separable real Hilbert space, we study the problem of minimizing a convex function with Lipschitz continuous gradient in the presence of noisy evaluations. To this end, we associate a stochastic Heavy Ball system, incorporating a…

We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying index, along with a new {\em Regularized…

This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…

Non-smoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be…

In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we…

In this paper, we study a speed restart scheme for an inertial system with Hessian-driven damping. We establish a linear convergence rate for the function values along the restarted trajectories without assuming the strong convexity of the…

This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning…

We introduce a new model of the nonlocal wave equations with a logarithmic damping mechanism. We consider the Cauchy poroblem for the new model in the whole space. We study the asymptotic profile and optimal decay and blowup rates of…

In a Hilbert framework, for convex differentiable optimization, we consider accelerated gradient methods obtained by combining temporal scaling and averaging techniques with Tikhonov regularization. We start from the continuous steepest…

We propose a novel feasible-path algorithm to solve the optimal power flow (OPF) problem for real-time use cases. The method augments the seminal work of Dommel and Tinney with second-order derivatives to work directly in the reduced space…

We propose a penalty-based smoothing framework for convex nonsmooth functions with a supremum structure. The regularization yields a differentiable surrogate with controlled approximation error, a single-valued dual maximizer, and explicit…

Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…

We study the problem of the minimum-time damping of a closed string under a bounded load, applied at a single fixed point. A constructive feedback control law is designed, which allows bringing the system to a bounded neighbourhood of the…

This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as…

Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle lower bounds. But their heuristic construction has hindered…

We introduce a new restarting scheme for a continuous inertial dynamics with Hessian driven-damping, and establish a linear convergence rate for the function values along the restarted trajectories. The proposed routine is implemented…

This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by…

In Hilbert space, we propose a family of primal-dual dynamical system for affine constrained convex optimization problem. Several damping coefficients, time scaling coefficients, and perturbation terms are thus considered. By constructing…