Related papers: Fast Convergence of Multiobjective Inertial Gradie…
Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…
There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
Our approach is part of the close link between continuous dissipative dynamical systems and optimization algorithms. We aim to solve convex minimization problems by means of stochastic inertial differential equations which are driven by the…
In this paper, we explore a specific optimization problem that combines a differentiable nonconvex function with a nondifferentiable function for multi-block variables, which is particularly relevant to tackle the multilinear…
The incremental gradient method is a prominent algorithm for minimizing a finite sum of smooth convex functions, used in many contexts including large-scale data processing applications and distributed optimization over networks. It is a…
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. Progress is measured by the Pareto stationarity gap $\mathcal{G}(x)$, the norm of the best convex…
In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…
In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can…
We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…
In this work, we approach the minimization of a continuously differentiable convex function under linear equality constraints by a second-order dynamical system with an asymptotically vanishing damping term. The system under consideration…
We analyze the convergence rate of the multiplicative gradient (MG) method for PET-type problems with $m$ component functions and an $n$-dimensional optimization variable. We show that the MG method has an $O(\ln(n)/t)$ convergence rate, in…
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…
In a Hilbert space setting, for convex optimization, we show the convergence of the iterates to optimal solutions for a class of accelerated first-order algorithms. They can be interpreted as discrete temporal versions of an inertial…
We consider a generic min-max multi-objective bilevel optimization problem with applications in robust machine learning such as representation learning and hyperparameter optimization. We design MORBiT, a novel single-loop gradient…
Many modern machine learning applications, such as multi-task learning, require finding optimal model parameters to trade-off multiple objective functions that may conflict with each other. The notion of the Pareto set allows us to focus on…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step…
In this article, we extend our previous work (Applicable Analysis, 2024, pp. 1-25) on the steepest descent method for uncertain multiobjective optimization problems. While that study established local convergence, it did not address global…