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A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…

Optimization and Control · Mathematics 2018-01-22 Raino A. E. Mäkinen

We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state…

Optimization and Control · Mathematics 2024-03-06 Eduardo Casas , Konstantinos Chrysafinos , Mariano Mateos

We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure…

Optimization and Control · Mathematics 2026-04-09 Drew P. Kouri

In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…

Optimization and Control · Mathematics 2024-12-26 Hong Zhu

We study a class of monotone inclusions called "self-concordant inclusion" which covers three fundamental convex optimization formulations as special cases. We develop a new generalized Newton-type framework to solve this inclusion. Our…

Optimization and Control · Mathematics 2017-07-25 Quoc Tran-Dinh , Tianxiao Sun , Shu Lu

This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning, where the primary design objective is to minimize the…

Optimization and Control · Mathematics 2017-04-24 Richard C. Barnard , Christian Clason

In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…

Numerical Analysis · Mathematics 2019-05-16 Bangti Jin , Yifeng Xu , Jun Zou

Non-smooth regularization is widely used in image reconstruction to eliminate the noise while preserving subtle image structures. In this work, we investigate the use of proximal Newton (PN) method to solve an optimization problem with a…

Signal Processing · Electrical Eng. & Systems 2019-12-05 Tao Ge , Umberto Villa , Ulugbek S. Kamilov , Joseph A. O'Sullivan

The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…

Optimization and Control · Mathematics 2017-09-01 Yongfeng Li , Zaiwen Wen , Chao Yang , Yaxiang Yuan

We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the superlinear convergence of the semismooth Newton method for an optimal control problem governed by a…

Optimization and Control · Mathematics 2025-06-25 Casas Eduardo , Mateos Mariano

This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…

Numerical Analysis · Mathematics 2024-03-12 Pratibha Shakya

In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different set of constraints, namely (i) integral state constraint…

Optimization and Control · Mathematics 2021-08-09 Kamana Porwal , Pratibha Shakya

This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…

Numerical Analysis · Mathematics 2021-12-17 Thadeu A. Senne , Francisco A. M. Gomes , Sandra A. Santos

In this paper we investigate adaptive discretization of the iteratively regularized Gauss- Newton method IRGNM. All-at-once formulations considering the PDE and the measurement equation simultaneously allow to avoid (approximate) solution…

Numerical Analysis · Mathematics 2018-08-20 Barbara Kaltenbacher , Alana Kirchner , Boris Vexler

Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…

In path-following methods for conic programming knowledge of the performance of the (damped) Newton method at finite distances from the minimizer of a self-concordant function is crucial for the tuning of the parameters of the method. The…

Optimization and Control · Mathematics 2020-07-28 Roland Hildebrand

A class of exact penalty-type local search methods for optimal control problems with nonsmooth cost functional, nonsmooth (but continuous) dynamics, and nonsmooth state and control constraints is presented, in which the the penalty…

Optimization and Control · Mathematics 2023-02-21 M. V. Dolgopolik

In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…

Optimization and Control · Mathematics 2020-01-10 M. V. Dolgopolik , A. V. Fominyh

This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…

Optimization and Control · Mathematics 2025-06-25 Eduardo Casas , Konstantinos Chrysafinos , Mariano Mateos

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Optimization and Control · Mathematics 2025-05-08 Francisco Fuica , Nicolai Jork