Related papers: A Douglas-Rachford Splitting Method for Solving Mo…
In recent years, the Douglas-Rachford splitting method has been shown to be effective at solving many non-convex optimization problems. In this paper we present a local convergence analysis for non-convex feasibility problems and show that…
In this work, we introduce the notion of warped Yosida regularization and study the asymptotic behavior of the orbit of dynamical systems generated by warped Yosida regularization, which includes Douglas-Rachford dynamical system. We…
In this paper, we investigate the Douglas-Rachford method for two closed (possibly nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the Douglas-Rachford method converges locally with R-linear rate. In…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…
The deviation vectors provide additional degrees of freedom and effectively enhance the flexibility of algorithms. In the literature, the iterative schemes with deviations are constructed and their convergence analyses are performed on an…
The Douglas-Rachford algorithm can be represented as the fixed point iteration of a firmly nonexpansive operator. When the operator has no fixed points, the algorithm's iterates diverge, but the difference between consecutive iterates…
This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon…
We shed light on the structure of the "three-operator" version of the forward-Douglas--Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving only the…
We consider the problem of minimizing the sum of a convex function and a convex function composed with an injective linear mapping. For such problems, subject to a coercivity condition at fixed points of the corresponding Picard iteration,…
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…
This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…
In this paper we present two Douglas-Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest…
We formulate a new class of two-person zero-sum differential games, in a stochastic setting, where a specification on a target terminal state distribution is imposed on the players. We address such added specification by introducing…
Many problems in robotics involve multiple decision making agents. To operate efficiently in such settings, a robot must reason about the impact of its decisions on the behavior of other agents. Differential games offer an expressive…
Learning from a stream of tasks usually pits plasticity against stability: acquiring new knowledge often causes catastrophic forgetting of past information. Most methods address this by summing competing loss terms, creating gradient…
The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections…
We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications…
The Douglas-Rachford and Peaceman-Rachford algorithms have been successfully employed to solve convex optimization problems, or more generally find zeros of monotone inclusions. Recently, the behaviour of these methods in the inconsistent…
The primal-dual Douglas-Rachford method is a well-known algorithm to solve optimization problems written as convex-concave saddle-point problems. Each iteration involves solving a linear system involving a linear operator and its adjoint.…
The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable…