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We study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of…

Machine Learning · Computer Science 2026-01-28 Dai Hai Nguyen , Duc Dung Nguyen , Atsuyoshi Nakamura , Hiroshi Mamitsuka

This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the…

Optimization and Control · Mathematics 2026-02-10 Zeyi Xu , Long Chen

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

Optimization and Control · Mathematics 2015-06-12 Euhanna Ghadimi , Iman Shames , Mikael Johansson

This paper introduces a unified framework for accelerated gradient methods through the variable and operator splitting (VOS). The operator splitting decouples the optimization process into simpler subproblems, and more importantly, the…

Optimization and Control · Mathematics 2025-05-08 Long Chen , Luo Hao , Jingrong Wei

We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…

Optimization and Control · Mathematics 2024-04-18 Yunier Bello-Cruz , J. G. Melo , L. F. Prudente , R. V. G. Serra

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…

Optimization and Control · Mathematics 2022-02-09 Mert Gürbüzbalaban , Asuman Ozdaglar , Pablo Parrilo

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding…

Optimization and Control · Mathematics 2021-03-30 Konstantin Pieper , Daniel Walter

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

Machine Learning · Computer Science 2023-08-22 Siyuan Xu , Minghui Zhu

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…

Optimization and Control · Mathematics 2022-09-15 David Alexander Hulett , Dang-Khoa Nguyen

In this work, we study the computational complexity of reducing the squared gradient magnitude for smooth minimax optimization problems. First, we present algorithms with accelerated $\mathcal{O}(1/k^2)$ last-iterate rates, faster than the…

Optimization and Control · Mathematics 2021-06-11 TaeHo Yoon , Ernest K. Ryu

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

The optimized gradient method (OGM) provides a factor-$\sqrt{2}$ speedup upon Nesterov's celebrated accelerated gradient method in the convex (but non-strongly convex) setup. However, this improved acceleration mechanism has not been well…

Optimization and Control · Mathematics 2021-05-25 Chanwoo Park , Jisun Park , Ernest K. Ryu

An Adagrad-inspired class of algorithms for smooth unconstrained optimization is presented in which the objective function is never evaluated and yet the gradient norms decrease at least as fast as $\calO(1/\sqrt{k+1})$ while second-order…

Optimization and Control · Mathematics 2023-02-16 S. Gratton , Ph. L. Toint

The multi-gradient descent algorithm (MGDA) finds a common descent direction that can improve all objectives by identifying the minimum-norm point in the convex hull of the objective gradients. This method has become a foundational tool in…

Optimization and Control · Mathematics 2025-04-16 Yuan-Zheng Lei , Yaobang Gong , Xianfeng Terry Yang

We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…

Machine Learning · Statistics 2015-04-08 Nicolas Flammarion , Francis Bach

In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form $\alpha/t$. For positive values of $\alpha$,…

Optimization and Control · Mathematics 2023-12-12 Tejas Natu , Camille Castera , Jalal Fadili , Peter Ochs

This work considers gradient descent for L-smooth convex optimization with stepsizes larger than the classic regime where descent can be ensured. The stepsize schedules considered are similar to but differ slightly from the recent silver…

Optimization and Control · Mathematics 2024-04-15 Benjamin Grimmer , Kevin Shu , Alex L. Wang

This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter…

Optimization and Control · Mathematics 2024-12-31 Chengzhi Huang , Jian Chen , Liping Tang

In this paper we propose stochastic gradient-free methods and accelerated methods with momentum for solving stochastic optimization problems. All these methods rely on stochastic directions rather than stochastic gradients. We analyze the…

Optimization and Control · Mathematics 2020-01-15 Xiaopeng Luo , Xin Xu

In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for…

Optimization and Control · Mathematics 2018-08-02 Sebastian Peitz , Michael Dellnitz