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A simplified conjugation scheme for lower semi-continuous functions. (English) Zbl 1383.49026

Summary: We present two generalized conjugation schemes for lower semi-continuous functions defined on a real Banach space whose norm is Fréchet differentiable off the origin, and sketch their applications to optimization duality theory. Both approaches are based upon a new characterization of lower semi-continuous functions as pointwise suprema of a special class of continuous functions.

MSC:

49J53 Set-valued and variational analysis
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
49J52 Nonsmooth analysis
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