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We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…

Optimization and Control · Mathematics 2018-08-20 Ahmad Ahmad Ali , Michael Hinze

We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a robust full-space interior-point (IP)-Gauss-Newton…

Optimization and Control · Mathematics 2024-10-22 Tucker Hartland , Cosmin G. Petra , Noemi Petra , Jingyi Wang

We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…

Analysis of PDEs · Mathematics 2012-10-16 Guillaume Bal , Matias Courdurier

In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable…

Optimization and Control · Mathematics 2021-08-17 Bowen Yi , Ruigang Wang , Ian R. Manchester

We address the problem of preconditioning a sequence of saddle point linear systems arising in the solution of PDE-constrained optimal control problems via active-set Newton methods, with control and (regularized) state constraints. We…

Numerical Analysis · Mathematics 2015-05-25 Margherita Porcelli , Valeria Simoncini , Mattia Tani

We present a new parallel computational framework for the efficient solution of a class of $L^2$/$L^1$-regularized optimal control problems governed by semi-linear elliptic partial differential equations (PDEs). The main difficulty in…

Optimization and Control · Mathematics 2025-08-20 Gabriele Ciaramella , Michael Kartmann , Georg Müller

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…

Optimization and Control · Mathematics 2008-05-13 Xinjia Chen , Kemin Zhou

The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…

Optimization and Control · Mathematics 2024-02-14 Peng Luo , Alexander Schied , Xiaole Xue

This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage…

Systems and Control · Computer Science 2017-11-30 Karthik Elamvazhuthi , Hendrik Kuiper , Spring Berman

In this work, we study data preconditioning, a well-known and long-existing technique, for boosting the convergence of first-order methods for regularized loss minimization. It is well understood that the condition number of the problem,…

Numerical Analysis · Computer Science 2015-09-28 Tianbao Yang , Rong Jin , Shenghuo Zhu , Qihang Lin

Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…

Optimization and Control · Mathematics 2015-11-06 Anna Fiedler , Fabian J. Theis , Jan Hasenauer

We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…

Numerical Analysis · Mathematics 2025-03-18 Fernando Gaspoz , Christian Kreuzer , Andreas Veeser , Winnifried Wollner

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…

Optimization and Control · Mathematics 2021-06-18 Caroline Geiersbach , Winnifried Wollner

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Machine Learning · Computer Science 2024-01-24 Alexandre d'Aspremont , Cristóbal Guzmán , Clément Lezane

We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…

Systems and Control · Electrical Eng. & Systems 2020-07-22 Edouard Leurent , Denis Efimov , Odalric-Ambrym Maillard

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…

Optimization and Control · Mathematics 2022-10-31 Alberto De Marchi

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…

Machine Learning · Computer Science 2024-10-03 Vincenzo Di Vito , Mostafa Mohammadian , Kyri Baker , Ferdinando Fioretto

In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…

Optimization and Control · Mathematics 2022-05-18 Eduardo Casas , Mariano Mateos

Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which…

Optimization and Control · Mathematics 2024-12-03 Tristan van Leeuwen , Yunan Yang

Data-driven predictive control methods based on the Willems' fundamental lemma have shown great success in recent years. These approaches use receding horizon predictive control with nonparametric data-driven predictors instead of…

Systems and Control · Electrical Eng. & Systems 2023-12-06 Mingzhou Yin , Andrea Iannelli , Roy S. Smith