A Theory of Optimization and Optimal Control for Nonlinear Evolution and Singular Equations: Applications to Nonlinear Partial Differential Equations

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World Scientific, 1990 - Mathematics - 274 pages
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This research monograph offers a general theory which encompasses almost all known general theories in such a way that many practical applications can be obtained. It will be useful for mathematicians interested in the development of the abstract Control Theory with applications to Nonlinear PDE, as well as physicists, engineers, and economists looking for theoretical guidance in solving their optimal control problems; and graduate-level seminar courses in nonlinear applied functional analysis.
 

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Contents

A MAXIMAL ELEMENT PRINCIPLE FOR CONSTRAINT SETS
1
Nonlinear Evolution Equations as Constraints
11
GLIMla
18
Elliptic Regularization
31
Smoothing Operators Combined with Elliptic
40
Existence of Tangent Directions
47
Solving Nonlinear Evolution Equations
55
Existence of Tangent Directions via GLIMII lia
61
Smoothing Operators Combined with Elliptic
140
OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
148
Smoothing Operators Combined with Elliptic
154
Smoothing Operators Combined with Elliptic
162
GLIMIIIa
170
Existence of Tangent Directions via GLIMIII
176
Smoothing Operators and Elliptic Regularization
182
Tangent Directions for Optimal Control
188

Contents
66
GLIMIIIa
77
Elliptic Regularization and Convex Approximate
85
Smoothing Operators and Elliptic Regularization
95
Tangent Directions involving Control Functions
101
SMOOTHING OPERATORS WITHOUT ELLIPTIC REGULARIZATION
107
Smoothing Operators and GLIMIb
113
OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
120
Smoothing Operators Combined with Elliptic
127
Existence of Tangent Directions
134
Contents
191
An Extremum Principle
198
OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
236
Existence of Tangent Directions for Nonlinear
243
Tangent Directions for Controlled Nonlinear
249
Existence of Tangent Directions for Nonlinear
256
Contents
263
Optimal Control with Nondifferentiable Objective
269
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