Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/l-documentclass-12pt-minimal-usepackage-amsmath-usepackage-wasysym-M0IBwzNXiy
References (24)
-
W. Alt, R. Griesse, N. Metla, A. Rösch (2010)
Lipschitz stability for elliptic optimal control problems with mixed control-state constraintsOptimization, 59
-
A. Jourani (1993)
Regularity and strong sufficient optimality conditions in differentiable optimization problemsNumerical Functional Analysis and Optimization, 14
-
BT Kien, J-C Yao (2017)
Local stability of solutions to parametric semilinear elliptic optimal control problemsAppl. Anal. Optim., 1
-
N. Son, B. Kien, A. Rösch (2016)
Second-Order Optimality Conditions for Boundary Control Problems with Mixed Pointwise ConstraintsSIAM J. Optim., 26
-
I. Kuzmanovic, N. Truhar (2013)
Optimization of the solution of the parameter-dependent Sylvester equation and applicationsJ. Comput. Appl. Math., 237
-
J. Bonnans, A. Shapiro (2000)
Perturbation Analysis of Optimization Problems -
R Griesse (2006)
Lipschitz stability of solutions to some state-constrained elliptic optimal control problemsJ. Anal. Appl., 25
-
B. Kien, V. Nhu (2014)
Second-Order Necessary Optimality Conditions for a Class of Semilinear Elliptic Optimal Control Problems with Mixed Pointwise ConstraintsSIAM J. Control. Optim., 52
-
V. Nhu, N. Auh, B. Kien (2013)
HÖLDER CONTINUITY OF THE SOLUTION MAP TO AN ELLIPTIC OPTIMAL CONTROL PROBLEM WITH MIXED CONSTRAINTSTaiwanese Journal of Mathematics, 17
-
P. Grisvard (1985)
Elliptic Problems in Nonsmooth Domains -
B. Kien, V. Nhu, A. Rösch (2015)
Lower semicontinuity of the solution map to a parametric elliptic optimal control problem with mixed pointwise constraintsOptimization, 64
-
R. Griesse, N. Metla, A. Rösch (2008)
Convergence analysis of the SQP method for nonlinear mixed‐constrained elliptic optimal control problemsZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 88
-
H. Brezis (2010)
Functional Analysis, Sobolev Spaces and Partial Differential Equations -
R. Griesse (2006)
Lipschitz Stability of Solutions to Some State-Constrained Elliptic Optimal Control ProblemsZeitschrift Fur Analysis Und Ihre Anwendungen, 25
-
(1972)
Probl‘emes unilateraux -
A. Jourani (1994)
Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraintsJournal of Optimization Theory and Applications, 81
-
J. Zowe, S. Kurcyusz (1979)
Regularity and stability for the mathematical programming problem in Banach spacesApplied Mathematics and Optimization, 5
-
K. Malanowski (2001)
Solutions Differentiability of Parametric Optimal Control for Elliptic Equations -
W. Alt (1991)
Local stability of solutions to differentiable optimization problems in banach spacesJournal of Optimization Theory and Applications, 70
-
B. Kien, V. Nhu, N. Son (2016)
Second-Order Optimality Conditions for a Semilinear Elliptic Optimal Control Problem with Mixed Pointwise ConstraintsSet-Valued and Variational Analysis, 25
-
B. Kien (2018)
Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes EquationsActa Mathematica Vietnamica, 44
-
Kazufumi Ito, K. Kunisch (1992)
Sensitivity analysis of solutions to optimization problems in Hilbert spaces with applications to optimal control and estimationJournal of Differential Equations, 99
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
M. Hinze, C. Meyer (2012)
Stability of semilinear elliptic optimal control problems with pointwise state constraintsComputational Optimization and Applications, 52
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer Science+Business Media, LLC, part of Springer Nature 2020
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-020-09664-5
- Publisher site
- See Article on Publisher Site
Abstract
This paper studies local stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints. We show that if the unperturbed problem satisfies the strictly nonnegative second-order optimality conditions, then the solution map is upper Hölder continuous in L∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^\infty $$\end{document}-norm of control variable.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Mar 3, 2020
Keywords: Solution stability; Locally Hölder upper continuity; Optimality condition; Second-order sufficient optimality condition; 49K15; 90C29