Elias, Leonardo M.; Martínez-Legaz, Juan E. A simplified conjugation scheme for lower semi-continuous functions. (English) Zbl 1383.49026 Optimization 65, No. 4, 751-763 (2016). 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. Cited in 2 Documents 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 Keywords:lower semi-continuous function; generalized convex conjugation; optimization duality theory PDFBibTeX XMLCite \textit{L. M. Elias} and \textit{J. E. Martínez-Legaz}, Optimization 65, No. 4, 751--763 (2016; Zbl 1383.49026) Full Text: DOI Link References: [1] DOI: 10.1080/02331934.2010.507273 · Zbl 1257.90071 · doi:10.1080/02331934.2010.507273 [2] Leonard IE, Trans. Amer. Math. Soc 198 pp 229– (1974) [3] Phelps RR, Convex functions, monotone operators and differentiability (1993) [4] Stromberg KR, Introduction to classical real analysis (1981) [5] Penot J-P, Optimization 64 pp 473– (2015) [6] DOI: 10.1007/s10957-013-0375-8 · Zbl 1295.47009 · doi:10.1007/s10957-013-0375-8 [7] DOI: 10.1007/0-387-23393-8_6 · doi:10.1007/0-387-23393-8_6 [8] DOI: 10.1007/978-1-4757-3200-9 · doi:10.1007/978-1-4757-3200-9 [9] Singer I, Abstract convex analysis (1997) [10] DOI: 10.1007/978-3-642-02431-3 · Zbl 0888.49001 · doi:10.1007/978-3-642-02431-3 [11] DOI: 10.1007/BF01584656 · Zbl 0259.90032 · doi:10.1007/BF01584656 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.