Related papers: Computational Method for Desensitized Optimal Guid…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
We propose a method to enhance 3D Gaussian Splatting (3DGS)~\cite{Kerbl2023}, addressing challenges in initialization, optimization, and density control. Gaussian Splatting is an alternative for rendering realistic images while supporting…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
Inertial-aided systems require continuous motion excitation among other reasons to characterize the measurement biases that will enable accurate integration required for localization frameworks. This paper proposes the use of informative…
We present a distributed conjugate gradient method for distributed optimization problems, where each agent computes an optimal solution of the problem locally without any central computation or coordination, while communicating with its…
We apply a novel method with machine learning to calibrate sub-grid models within numerical simulation codes to achieve convergence with observations and between different codes. It utilizes active learning and neural density estimators.…
Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…
The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this…
Training deep neural network is a high dimensional and a highly non-convex optimization problem. Stochastic gradient descent (SGD) algorithm and it's variations are the current state-of-the-art solvers for this task. However, due to…
We analyze a time-coarsening strategy for model predictive control (MPC) that we call diffusing-horizon MPC. This strategy seeks to overcome the computational challenges associated with optimal control problems that span multiple…
We propose a path planning methodology for a mobile robot navigating through an obstacle-filled environment to generate a reference path that is traceable with moderate sensing efforts. The desired reference path is characterized as the…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
In the realm of autonomous driving, accurately detecting surrounding obstacles is crucial for effective decision-making. Traditional methods primarily rely on 3D bounding boxes to represent these obstacles, which often fail to capture the…
Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized,…
A robust drift-safe rendezvous trajectory optimization tool is developed in this work, with applications to orbital rendezvous and proximity operations. The method is based on direct collocation and utilizes a sequential convex programming…
In decentralized optimization over networks, synchronizing the updates of all nodes incurs significant communication overhead. For this reason, much of the recent literature has focused on the analysis and design of asynchronous…
This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the…