相关论文: Tracking solutions of time-varying variational ine…

Time-varying optimization problems are central to many engineering applications, where performance metrics and system constraints evolve dynamically with time. Several algorithms have been proposed to address these problems; a common…

In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is…

In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…

Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…

This paper develops an algorithmic framework for tracking fixed points of time-varying contraction mappings. Analytical results for the tracking error are established for the cases where: (i) the underlying contraction self-map changes at…

We leverage best response dynamics to solve monotone variational inequalities on compact and convex sets. Specialization of the method to variational inequalities in game theory recovers convergence results to Nash equilibria when agents…

A major limitation of online algorithms that track the optimizers of time-varying nonconvex optimization problems is that they focus on a specific local minimum trajectory, which may lead to poor spurious local solutions. In this paper, we…

Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…

Algorithms that solve zero-sum games, multi-objective agent objectives, or, more generally, variational inequality (VI) problems are notoriously unstable on general problems. Owing to the increasing need for solving such problems in machine…

We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…

Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…

The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…

This paper considers a class of convex optimization problems where both, the objective function and the constraints, have a continuously varying dependence on time. Our goal is to develop an algorithm to track the optimal solution as it…

Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…

Optimization problems emerging in most of the real-world applications are dynamic, where either the objective function or the constraints change continuously over time. This paper proposes projected primal-dual dynamical system approaches…

Feedback optimization has emerged as a promising approach for regulating dynamical systems to optimal steady states that are implicitly defined by underlying optimization problems. Despite their effectiveness, existing methods face two key…

This paper presents a decentralized algorithm for a team of agents to track time-varying fixed points that are the solutions to time-varying convex optimization problems. The algorithm is first-order, and it allows for total asynchrony in…

Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…

We study monotone variational inequalities that can arise as optimality conditions for constrained convex optimisation or convex-concave minimax problems and propose a novel algorithm that uses only one gradient/operator evaluation and one…

Variational inequalities (VIs) are a broad class of optimization problems encompassing machine learning problems ranging from standard convex minimization to more complex scenarios like min-max optimization and computing the equilibria of…