Full Record

Author | Mejeur, Joel M. |

Title | Function Space Nonlinear Rescaling Methods for Elliptic Control Problems with Point-wise State and Control Constraints |

URL | http://hdl.handle.net/1920/11279 |

Publication Date | 2017 |

Date Accessioned | 2018-10-22 01:19:54 |

University/Publisher | George Mason University |

Abstract | State inequality constraints in PDE Constrained Optimization (PDECO) arise in many areas of science and engineering. Unfortunately these constraints, and the resulting Lagrange multipliers, are known to negatively influence the behavior of many existing optimization methods. |

Subjects/Keywords | Applied mathematics; Augmented Lagrangian; Control Constraints; Elliptic Control; Nonlinear Rescaling; PDE Constrained Optimization; State Constraints |

Contributors | Griva, Igor (advisor) |

Language | en |

Rights | Copyright 2017 Joel M. Mejeur |

Country of Publication | us |

Record ID | handle:1920/11279 |

Repository | gmu |

Date Retrieved | 2020-01-02 |

Date Indexed | 2020-01-06 |

Issued Date | 2017-01-01 00:00:00 |

Sample Search Hits | Sample Images | Cited Works

…*constraints* in *PDE* Constrained Optimization (PDECO) arise in
many areas of science and engineering. Unfortunately these *constraints*, and the resulting Lagrange multipliers, are known to negatively influence the behavior of many
existing optimization…

…construct and solve the discretized version
of the inner iteration.
Chapter 1: Introduction
The field of optimization for problems with Partial Differential Equation (*PDE*) *constraints* has been an active area of research for many decades, which…

…problem with point-wise
inequality *constraints* both the state and control leads to 5 times the number of discretized degrees of freedom than just the *PDE* alone. One additional detail is that
efficient solvers may exist for finding the solution to the…

…discretized *PDE*, and linear systems that may arise from the optimization problem are often more complex,
requiring different preconditioning and solution strategies.
PDECO problems which contain point-wise inequality *constraints* on the state
variables pose…

…2.1
Problem Statement and Notation
The general optimization problem examined here is a stationary optimal control problem with an elliptic *PDE* constraint, with independent inequality *constraints* on the
state and control variables. Optimization…

…problems do often arise with these *PDE*
*constraints*. Elliptic *constraints* are also more amenable for analysis due to the well
behaved and well studied qualities of the elliptic *PDE*.
Let J(u, q) be the functional being minimized, where u is the…

…List of Tables
Table
Page
7.1
7.2
State and Control *Constraints* . . . . . . . . . . . . . . . . . . . . . . 103
State Constraint Only . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.3
Control Constraint Only…

…105
vii
Abstract
FUNCTION SPACE NONLINEAR RESCALING METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH POINT-WISE STATE AND CONTROL *CONSTRAINTS*
Joel M Mejeur, PhD
George Mason University, 2017
Dissertation Director: Dr. Igor Griva
State inequality…