Related papers: Efficient preconditioners for solving dynamical op…
This paper proposes a collocation boundary element method based on the Burton--Miller method for solving transmission problems, which is rapidly convergent within the Krylov subspace solver framework. Our study enhances Burton--Miller-type…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…
We propose the Steiner Traveling Salesman Problem with Time Windows and Pickup and Delivery, an advanced and practical extension of classical routing models. This variant integrates the characteristics of the Steiner Traveling Salesman…
This paper investigates an efficient algorithm for trajectory planning problem of autonomous unmanned aerial vehicles which fly over three-dimensional terrains. The proposed algorithm combines convex optimization with disjunctive…
The importance of Schur complement based preconditioners are well-established for classical saddle point problems in $\mathbb{R}^N \times \mathbb{R}^M$. In this paper we extend these results to multiple saddle point problems in Hilbert…
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path.…
The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system at each time-step. This work develops a fully robust and…
Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples and where the goal is to find the closest map to the ground…
Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…
As a core part of autonomous driving systems, motion planning has received extensive attention from academia and industry. However, real-time trajectory planning capable of spatial-temporal joint optimization is challenged by nonholonomic…
We consider the problem of iteratively solving large and sparse double saddle-point systems arising from the stationary Stokes-Darcy equations in two dimensions, discretized by the Marker-and-Cell (MAC) finite difference method. We analyze…
In this paper, we extend the idea of using controlled perturbations to enhance the capabilities of active-set prediction for interior point methods for convex Quadratic Programming (QP) problems. Namely, we consider perturbing the…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This paper proposes a primal active-set strategy (PRESAS) for the efficient solution…
This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…
The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled…
Safety-guaranteed motion planning is critical for self-driving cars to generate collision-free trajectories. A layered motion planning approach with decoupled path and speed planning is widely used for this purpose. This approach is prone…
We propose an efficient way of solving optimal control problems for rigid-body systems on the basis of inverse dynamics and the multiple-shooting method. We treat all variables, including the state, acceleration, and control input torques,…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…