Related papers: Invariant Smoothing on Lie Groups
In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…
Localization and mapping with heterogeneous multi-sensor fusion have been prevalent in recent years. To adequately fuse multi-modal sensor measurements received at different time instants and different frequencies, we estimate the…
In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…
We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…
Accurate state estimation for robotic systems evolving on Lie group manifolds, such as legged robots, is a prerequisite for achieving agile control. However, this task is challenged by nonlinear observation models defined on curved…
Many navigation problems can be formulated as observer design on linear observed systems with a two-frame group structure, on which an invariant filter can be implemented with guaranteed consistency and stability. It's still unclear how…
This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
In this brief paper, we present a naive aggregation algorithm for a typical learning problem with expert advice setting, in which the task of improving generalization, i.e., model validation, is embedded in the learning process as a…
This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of…
The group synchronization problem involves estimating a collection of group elements from noisy measurements of their pairwise ratios. This task is a key component in many computational problems, including the molecular reconstruction…
This paper presents an invariant Rauch-Tung- Striebel (IRTS) smoother applicable to systems with states that are an element of a matrix Lie group. In particular, the extended Rauch-Tung-Striebel (RTS) smoother is adapted to work within a…