Related papers: Iterative scheme for solving optimal transportatio…
We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed…
In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow…
Mixed integer linear programming (MILP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Due to dispersion, light with different wavelengths, or colors, is refracted at different angles. Our purpose is to determine when is it possible to design a lens made of a single homogeneous material so that it refracts light superposition…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…
This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, the proposed method…
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…
The optimal design of multi-target rendezvous and flyby missions is challenging due to the combination of traditional spacecraft trajectory optimization and high-dimensional combinatorial problems. This often requires large-scale global…
Platooning of vehicles is a promising approach for reducing fuel consumption, increasing vehicle safety, and using road space more efficiently. We consider the important but difficult problem of assigning optimal routes and departure…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel…
This paper presents a spatial-based trajectory planning method for automated vehicles under actuator, obstacle avoidance, and vehicle dimension constraints. Starting from a nonlinear kinematic bicycle model, vehicle dynamics are transformed…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
Recently, the joint design of optical systems and downstream algorithms is showing significant potential. However, existing rays-described methods are limited to optimizing geometric degradation, making it difficult to fully represent the…
We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and…
This research focuses on trajectory planning problems for autonomous vehicles utilizing numerical optimal control techniques. The study reformulates the constrained optimization problem into a nonlinear programming problem, incorporating…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…