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

DOI:
https://doi.org/10.1090/S0002-9947-98-01984-9

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:
https://doi.org/10.1090/S0002-9947-98-01984-9

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