Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming

We develop various (exact) calculus rules for Fréchet lower and upper subgradients of extended-real-valued functions in real Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimiza...

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Vydané v:Optimization Ročník 55; číslo 5-6; s. 685 - 708
Hlavní autori: Mordukhovich, B. S., Nam, N. M., Yen, N. D.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia Taylor & Francis Group 01.10.2006
Taylor & Francis LLC
Predmet:
Calculus
Coderivatives
Difference-type functions
Fréchet normals
Geometric and operator constraints
Mathematical functions
Mathematics Subject Classifications 2000
Necessary optimality conditions
Optimization
Primary: 49J52
Secondary: 90C30
Studies
Subdifferential calculus
Subgradients
Variational analysis and constrained optimization
Weak sharp minima
ISSN:0233-1934, 1029-4945
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Abstract We develop various (exact) calculus rules for Fréchet lower and upper subgradients of extended-real-valued functions in real Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima. §Dedicated to Diethard Pallaschke in honor of his 65th birthday.
AbstractList We develop various (exact) calculus rules for Fréchet lower and upper subgradients of extended-real-valued functions in real Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima. [PUBLICATION ABSTRACT]
We develop various (exact) calculus rules for Fréchet lower and upper subgradients of extended-real-valued functions in real Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima. §Dedicated to Diethard Pallaschke in honor of his 65th birthday.
Author Mordukhovich, B. S.
Yen, N. D.
Nam, N. M.
Author_xml – sequence: 1
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– sequence: 2
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  surname: Nam
  fullname: Nam, N. M.
  organization: Department of Mathematics , Wayne State University
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  givenname: N. D.
  surname: Yen
  fullname: Yen, N. D.
  organization: Institute of Mathematics
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Cites_doi 10.1007/978-94-015-9920-7
10.1515/9781400873173
10.1137/0331063
10.1023/A:1008233531797
10.1007/978-3-642-02431-3
10.1023/A:1023673105317
10.1007/3-540-31246-3
10.1007/3-540-31247-1
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References Phelps RR (CIT0009) 1993
Polyak BT (CIT0010) 1987
Mordukhovich BS (CIT0005) 2006
CIT0012
Pallaschke D (CIT0007) 2002
CIT0002
Borwein JM (CIT0001) 2005
CIT0004
Rockafellar RT (CIT0011) 1970
Mordukhovich BS (CIT0006) 2006
Hiriart-Urruty J-B (CIT0003) 1985; 256
CIT0008
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Snippet We develop various (exact) calculus rules for Fréchet lower and upper subgradients of extended-real-valued functions in real Banach spaces. Then we apply this...
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SubjectTerms Calculus
Coderivatives
Difference-type functions
Fréchet normals
Geometric and operator constraints
Mathematical functions
Mathematics Subject Classifications 2000
Necessary optimality conditions
Optimization
Primary: 49J52
Secondary: 90C30
Studies
Subdifferential calculus
Subgradients
Variational analysis and constrained optimization
Weak sharp minima
Title Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming
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