Gradient-Related Constrained Minimization Algorithms in Function Spaces: Convergence Properties and Computational Implications

1994 ◽  
pp. 95-114 ◽  
Author(s):  
Joseph C. Dunn
Keyword(s):  
Function Spaces ◽  
Constrained Minimization ◽  
Convergence Properties ◽  
Minimization Algorithms

scholarly journals Convergence Properties of Minimization Algorithms for Convex Constraints Using a Structured Trust Region

1996 ◽  
Vol 6 (4) ◽  
pp. 1059-1086 ◽  
Author(s):  
A. R. Conn ◽  
Nick Gould ◽  
A. Sartenaer ◽  
Ph. L. Toint
Keyword(s):  
Trust Region ◽  
Convex Constraints ◽  
Convergence Properties ◽  
Minimization Algorithms

scholarly journals ON SOME CLASSES OF OPERATORS DETERMINED BY THE STRUCTURE OF THEIR MEMORY

2002 ◽  
Vol 45 (2) ◽  
pp. 467-490 ◽  
Author(s):  
Mikhail E. Drakhlin ◽  
Arcady Ponosov ◽  
Eugene Stepanov
Keyword(s):  
Primary 47B38 ◽  
Function Spaces ◽  
Subject Classification ◽  
Local Operator ◽  
Convergence Properties ◽  
Lebesgue Spaces ◽  
Nonlinear Operators ◽  
Conditional Expectations ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractTwo classes of nonlinear operators generalizing the notion of a local operator between ideal function spaces are introduced. The first class, called atomic, contains in particular all the linear shifts, while the second one, called coatomic, contains all the adjoints to former, and, in particular, the conditional expectations. Both classes include local (in particular, Nemytski\v{\i}) operators and are closed with respect to compositions of operators. Basic properties of operators of introduced classes in the Lebesgue spaces of vector-valued functions are studied. It is shown that both classes inherit from Nemytski\v{\i} operators the properties of non-compactness in measure and weak degeneracy, while having different relationships of acting, continuity and boundedness, as well as different convergence properties. Representation results for the operators of both classes are provided. The definitions of the introduced classes as well as the proofs of their properties are based on a purely measure theoretic notion of memory of an operator, also introduced in this paper.AMS 2000 Mathematics subject classification: Primary 47B38; 47A67; 34K05

scholarly journals Constrained Minimization Algorithms

2013 ◽  
Vol 59 ◽  
pp. 303-324 ◽  
Author(s):  
H. Lantéri ◽  
C. Theys ◽  
C. Richard
Keyword(s):  
Constrained Minimization ◽  
Minimization Algorithms
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