Recent advances in trust region algorithms

Y Yuan - Mathematical Programming, 2015 - Springer
Trust region methods are a class of numerical methods for optimization. Unlike line search
type methods where a line search is carried out in each iteration, trust region methods …

Trust-region methods on Riemannian manifolds

PA Absil, CG Baker, KA Gallivan - Foundations of Computational …, 2007 - Springer
A general scheme for trust-region methods on Riemannian manifolds is proposed and
analyzed. Among the various approaches available to (approximately) solve the trust-region …

[图书][B] Computational optimization of systems governed by partial differential equations

A Borzì, V Schulz - 2011 - SIAM
This book provides an introduction to some modern computational techniques for
optimization problems governed by partial differential equations (PDEs). The optimization …

[图书][B] Optimale Steuerung partieller Differentialgleichungen

F Tröltzsch - 2005 - Springer
Die mathematische Optimierung von Vorgängen, die durch partielle Differentialgleichungen
modelliert werden, hat in den letzten Jahren einen beachtlichen Aufschwung genommen …

Adaptive h‐refinement for reduced‐order models

K Carlberg - International Journal for Numerical Methods in …, 2015 - Wiley Online Library
This work presents a method to adaptively refine reduced‐order models a posteriori without
requiring additional full‐order‐model solves. The technique is analogous to mesh‐adaptive …

Multigrid methods for PDE optimization

A Borzi, V Schulz - SIAM review, 2009 - SIAM
Research on multigrid methods for optimization problems is reviewed. Optimization
problems considered include shape design, parameter optimization, and optimal control …

Preconditioned all-at-once methods for large, sparse parameter estimation problems

E Haber, UM Ascher - Inverse Problems, 2001 - iopscience.iop.org
The problem of recovering a parameter function based on measurements of solutions of a
system of partial differential equations in several space variables leads to a number of …

A trust-region algorithm with adaptive stochastic collocation for PDE optimization under uncertainty

DP Kouri, M Heinkenschloss, D Ridzal… - SIAM Journal on …, 2013 - SIAM
The numerical solution of optimization problems governed by partial differential equations
(PDEs) with random coefficients is computationally challenging because of the large number …

Parallel Lagrange--Newton--Krylov--Schur methods for PDE-constrained optimization. Part II: The Lagrange--Newton solver and its application to optimal control of …

G Biros, O Ghattas - SIAM Journal on Scientific Computing, 2005 - SIAM
In part I of this article, we proposed a Lagrange--Newton--Krylov--Schur (LNKS) method for
the solution of optimization problems that are constrained by partial differential equations …

Inexact sequential quadratic optimization for minimizing a stochastic objective function subject to deterministic nonlinear equality constraints

FE Curtis, DP Robinson, B Zhou - arXiv preprint arXiv:2107.03512, 2021 - arxiv.org
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic
optimization problems in which the decision variables are constrained to satisfy equations …