Related papers: Invariant Smoothing on Lie Groups
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
For the linear inverse problem with sparsity constraints, the $l_0$ regularized problem is NP-hard, and existing approaches either utilize greedy algorithms to find almost-optimal solutions or to approximate the $l_0$ regularization with…
A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted…
In the last few years, the notion of symmetry has provided a powerful and essential lens to view several optimization or sampling problems that arise in areas such as theoretical computer science, statistics, machine learning, quantum…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past…
In this paper, we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed. We propose a correspondent mini-max problem for nonlinear regression and give a numerical…
It is well-known that training neural networks for image classification with empirical risk minimization (ERM) makes them vulnerable to relying on spurious attributes instead of causal ones for prediction. Previously, deep feature…
Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the…
Zero-shot diffusion posterior sampling offers a flexible framework for inverse problems by accommodating arbitrary degradation operators at test time, but incurs high computational cost due to repeated likelihood-guided updates. In…
In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on…
The system of generalized absolute value equations (GAVE) has attracted more and more attention in the optimization community. In this paper, by introducing a smoothing function, we develop a smoothing Newton algorithm with non-monotone…
Left-invariant optimal control problems on Lie groups form an important class of problems with big symmetry group. They are interesting from the theoretical point of view since they often can be completely studied, and general features can…
This paper proposes local exponential observers for systems on linear Lie groups. We study two different classes of systems. In the first class, the full state of the system evolves on a linear Lie group and is available for measurement. In…
We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting…
In this paper, we focus on finding the global minimizer of a general unconstrained nonsmooth nonconvex optimization problem. Taking advantage of the smoothing method and the consensus-based optimization (CBO) method, we propose a novel…
In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the overapproximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes" the dynamical characteristics of the…
Basing on some recently proposed methods for solving variational inequalities with non-smooth operators, we propose an analogue of the Mirror Prox method for the corresponding class of problems under the assumption of relative smoothness…
In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms…
The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use…