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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Necessary conditions
for constrained optimization problems
with semicontinuous and continuous data


Authors: Jonathan M. Borwein, Jay S. Treiman and Qiji J. Zhu
Journal: Trans. Amer. Math. Soc. 350 (1998), 2409-2429
MSC (1991): Primary 49J52; Secondary 49J40, 49J50, 58C20
MathSciNet review: 1433112
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.


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Additional Information

Jonathan M. Borwein
Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
Email: jborwein@cecm.sfu.ca

Jay S. Treiman
Affiliation: Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, Michigan 49008
Email: treiman@math-stat.wmich.edu

Qiji J. Zhu
Affiliation: Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, Michigan 49008
Email: zhu@math-stat.wmich.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01984-9
PII: S 0002-9947(98)01984-9
Keywords: Constrained optimization problems, multipliers, nonsmooth analysis, subderivatives, normals, fuzzy calculus
Received by editor(s): September 14, 1995
Received by editor(s) in revised form: August 9, 1996
Additional Notes: Research of the first author was supported by NSERC and by the Shrum Endowment at Simon Fraser University
Article copyright: © Copyright 1998 American Mathematical Society