Related papers: Primal-Dual Methods for Nonsmooth Nonconvex Optimi…
In this paper, we study stochastic constrained minimax optimization problems with nonconvex-nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its…
In this paper, we establish for the first time the oracle complexity of a Riemannian inexact augmented Lagrangian (RiAL) method with the classical dual update for solving a class of Riemannian nonsmooth composite problems. By using the…
This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…
Nonsmooth Riemannian optimization has attracted increasing attention, especially in problems with sparse structures. While existing formulations typically involve convex nonsmooth terms, incorporating nonsmooth difference-of-convex (DC)…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…
We study a class of optimization problems on Riemannian manifolds, where the objective function consists of a smooth term and quasi-norm type penalties with exponent $p \in (0, 1]$. The essential difficulty lies in the fact that the…
In this paper, we propose a variance-reduced primal-dual algorithm with Bregman distance for solving convex-concave saddle-point problems with finite-sum structure and nonbilinear coupling function. This type of problems typically arises in…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
We study the problem of minimizing the sum of a smooth function and a nonsmooth convex regularizer over a compact Riemannian submanifold embedded in Euclidean space. By introducing an auxiliary splitting variable, we propose an adaptive…
This paper considers a nonconvex optimization problem that evolves over time, and addresses the synthesis and analysis of regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized…
A transformed primal-dual (TPD) flow is developed for a class of nonlinear smooth saddle point system. The flow for the dual variable contains a Schur complement which is strongly convex. Exponential stability of the saddle point is…
We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective functionals and the resulting high-dimensional and…
In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…
Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
In this article we investigate the possibilities of accelerating the double smoothing technique when solving unconstrained nondifferentiable convex optimization problems. This approach relies on the regularization in two steps of the…
Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…
Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with…
By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…
In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…