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Title Function Space Nonlinear Rescaling Methods for Elliptic Control Problems with Point-wise State and Control Constraints
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Publication Date
Date Accessioned
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
Date Indexed 2020-01-06
Issued Date 2017-01-01 00:00:00

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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…

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…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…

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