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ESAIM: Proc., April 2007, Vol. 17, pp. 80-95
DOI: 10.1051/proc:071707
Exact calculus for proximal subgradients with applications to optimization
Boris S. Mordukhovich and Nguyen Mau NamDepartment of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.
(Published online: 26 April 2007)
Abstract
The paper contains new exact calculus rules
for proximal subgradients of extended-real-valued functions
defined on arbitrary real Banach spaces. We also develop efficient
formulas for evaluating proximal subgradients of marginal/value
functions in various problems of parametric optimization. The
results obtained are employed to derive new necessary optimality
conditions in unconstrained nondifferentiable programming.
Mathematics Subject Classification. 49J52, 49J53
Key words: Proximal normals, subgradients and coderivatives; Subdifferential calculus; Marginal and value functions; Weak sharp minima; Necessary optimality conditions; Banach spaces.
© EDP Sciences, ESAIM 2007
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