相关论文: A splitting proximal point method for Nash-Cournot…
We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time $O(\epsilon^{-7/4} \log(1/ \epsilon) )$ to find an $\epsilon$-stationary point,…
Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple…
We consider a distributed convex optimization problem in a network which is time-varying and not always strongly connected. The local cost function of each node is affected by some stochastic process. All nodes of the network collaborate to…
This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its…
We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We propose a splitting…
We consider for the first time a stochastic generalized Nash equilibrium problem, i.e., with expected-value cost functions and joint feasibility constraints, under partial-decision information, meaning that the agents communicate only with…
In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper-…
In this study, we consider an optimization problem with uncertainty dependent on decision variables, which has recently attracted attention due to its importance in machine learning and pricing applications. In this problem, the gradient of…
This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…
We consider the problem of computing an equilibrium in a class of \textit{nonlinear generalized Nash equilibrium problems (NGNEPs)} in which the strategy sets for each player are defined by equality and inequality constraints that may…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
Decentralized optimization is a promising parallel computation paradigm for large-scale data analytics and machine learning problems defined over a network of nodes. This paper is concerned with decentralized non-convex composite problems…
The distributed computation of equilibria and optima has seen growing interest in a broad collection of networked problems. We consider the computation of equilibria of convex stochastic Nash games characterized by a possibly nonconvex…
We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component,…
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
In this paper, we present a distributed algorithm for solving convex, constraint-coupled, optimization problems over peer-to-peer networks. We consider a network of processors that aim to cooperatively minimize the sum of local cost…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
It is well known that the projection method is not convergent for monotone equilibrium problems. Recently Sosa \textit{et al.} in \cite{SS2011} proposed a projection algorithm ensuring convergence for paramonotone equilibrium problems. In…