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In this paper we address the numerical solution of the quadratic optimal transport problem in its dynamical form, the so-called Benamou-Brenier formulation. When solved using interior point methods, the main computational bottleneck is the…

Numerical Analysis · Mathematics 2024-01-22 Enrico Facca , Gabriele Todeschi , Andrea Natale , Michele Benzi

PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\rm L^1$ term within the objective…

Optimization and Control · Mathematics 2019-02-13 John W. Pearson , Margherita Porcelli , Martin Stoll

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…

Numerical Analysis · Mathematics 2020-01-17 Karl Erik Holter , Miroslav Kuchta , Kent-Andre Mardal

In this paper, we execute the shift-splitting preconditioner for asymmetric saddle point problems with its (1,2) block's transposition unequal to its (2,1) block under the removed minus of its (2,1) block. The proposed preconditioner is…

Numerical Analysis · Mathematics 2021-09-13 Shi-Liang Wu , Davod Khojasteh Salkuyeh

We introduce a unified framework for computing approximately-optimal preconditioners for solving linear and non-linear systems of equations. We demonstrate that the condition number minimization problem, under structured transformations…

Optimization and Control · Mathematics 2025-12-09 M. Levent Doğan , Alperen Ergür , Elias Tsigaridas

The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context…

Pricing of Securities · Quantitative Finance 2013-02-18 Dylan Possamaï , Guillaume Royer , Nizar Touzi

Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…

Numerical Analysis · Mathematics 2016-09-06 L. Dykes , S. Noschese , L. Reichel

Poroelasticity problems play an important role in various engineering, geophysical, and biological applications. Their full discretization results in a large-scale saddle-point system at each time step that is becoming singular for locking…

Numerical Analysis · Mathematics 2025-06-27 Weizhang Huang , Zhuoran Wang

In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional…

Optimization and Control · Mathematics 2018-09-21 Yeojun Kim , Xiaojing Zhang , Jacopo Guanetti , Francesco Borrelli

This paper focuses on the energy-time optimal control of wheeled mobile robots undergoing point-to-point transitions in an obstacles free space. Two interchangeable models are used to arrive at the necessary conditions for optimality. The…

Robotics · Computer Science 2022-06-07 Youngjin Kim , Tarunraj Singh

In this paper, we propose a class of general second-order primal-dual dynamical systems with Tikhonov regularization and Hessian-driven damping for solving convex-concave bilinear saddle point problems. The proposed dynamical system…

Optimization and Control · Mathematics 2026-05-13 Bohan Zhang , Xiaojun Zhang

We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates…

Machine Learning · Computer Science 2017-04-13 Adams Wei Yu , Qihang Lin , Tianbao Yang

In this paper, we design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a structure-preserving finite-element approximation with…

Numerical Analysis · Mathematics 2016-05-03 James H. Adler , Xiaozhe Hu , Ludmil T. Zikatanov

In this article, we study the strong well-posedness, stability and optimal control of an incompressible magneto-viscoelastic fluid model in two dimensions. The model consists of an incompressible Navier--Stokes equation for the velocity…

Analysis of PDEs · Mathematics 2021-08-09 Harald Garcke , Patrik Knopf , Sourav Mitra , Anja Schlömerkemper

Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in Spatio-Temporal systems described by Partial Differential Equations (PDEs) among the robotics and control communities.…

Robotics · Computer Science 2021-02-19 Ethan N. Evans , Andrew P. Kendall , Evangelos A. Theodorou

The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…

Optimization and Control · Mathematics 2025-11-18 Alberto Domínguez Corella , Nicolai Jork , Vladimir M. Veliov

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the…

Numerical Analysis · Mathematics 2016-08-24 M. Cai , A. J. Nonaka , J. B. Bell , B. E. Griffith , A. Donev

We consider the optimal control of solutions of first order Hamilton-Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the propagation of a front by constructing an obstacle. We prove…

Optimization and Control · Mathematics 2013-10-11 Philip Jameson Graber

This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard/Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family…

Analysis of PDEs · Mathematics 2015-06-12 Michael Hintermüller , Tobias Keil , Donat Wegner

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…

Probability · Mathematics 2016-12-05 Giuseppina Guatteri