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In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…

Numerical Analysis · Mathematics 2017-10-18 Yan Luo , Zhu Wang

This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming (MICP) problems to global optimality. The proposed scheme uses an iterative…

Optimization and Control · Mathematics 2019-11-20 Alexander Murray , Timm Faulwasser , Veit Hagenmeyer , Mario E. Villanueva , Boris Houska

In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…

Optimization and Control · Mathematics 2021-11-23 Giacomo Borghi , Michael Herty , Lorenzo Pareschi

This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence of the residual at the predicted rate is investigated…

Numerical Analysis · Mathematics 2016-11-29 Sara Pollock

In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…

Optimization and Control · Mathematics 2016-08-29 Mahyar Fazlyab , Santiago Paternain , Victor M. Preciado , Alejandro Ribeiro

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

Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial differential equations (PDEs), they are computationally…

Numerical Analysis · Mathematics 2019-09-06 Howard C. Elman , Akwum Onwunta

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

Machine Learning · Computer Science 2021-10-27 Sifan Wang , Mohamed Aziz Bhouri , Paris Perdikaris

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…

Signal Processing · Electrical Eng. & Systems 2024-11-12 Junbin Liu , Ya Liu , Wing-Kin Ma , Mingjie Shao , Anthony Man-Cho So

An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…

Numerical Analysis · Mathematics 2021-07-21 Andreas Van Barel , Stefan Vandewalle

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…

We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

Optimization and Control · Mathematics 2023-10-10 Fangyuan Wang , Qiming Wang , Zhaojie Zhou

We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…

Numerical Analysis · Mathematics 2021-09-07 Enrique Otarola

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…

Numerical Analysis · Mathematics 2024-01-22 Anna Ivagnes , Nicola Demo , Gianluigi Rozza

We develop a fast and scalable computational framework to solve large-scale and high-dimensional Bayesian optimal experimental design problems. In particular, we consider the problem of optimal observation sensor placement for Bayesian…

Numerical Analysis · Mathematics 2020-11-09 Keyi Wu , Peng Chen , Omar Ghattas

This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…

Optimization and Control · Mathematics 2026-03-17 Ethan Foss , Simone D'Amico

We introduce a novel model based on the discrete optimal transport problem that incorporates congestion costs and replaces traditional constraints with weighted penalization terms. This approach better captures real-world scenarios…

Optimization and Control · Mathematics 2025-03-19 Marcelo Gallardo , Manuel Loaiza , Jorge Chávez

In this paper, we develop an analytical framework for the partial differential equation underlying the consensus-based optimization model. The main challenge arises from the nonlinear, nonlocal nature of the consensus point, coupled with a…

Analysis of PDEs · Mathematics 2025-04-16 Jinhuan Wang , Keyu Li , Hui Huang

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…

Numerical Analysis · Mathematics 2024-01-15 Maria Han Veiga , Lorenzo Micalizzi , Davide Torlo