Abstract
We present a duality formula for the (primed) problem
where \({g_1},{h_1},{g_2},{h_2}:X \to \overline {IR} \) are convex functions on the Hausdorff locally convex vector space X, with g2,h2 in Г (X).
Introducing a suitable dual problem defined from the Legendre-Fenchel conjugates of the data g 1, h 1, g 2, h 2, the duality formula establishes, under a standard qualification condition between g1 and h1, the zero gap between the two optimal values. Although unusual, the strict inequality in the constraint is crucial and convex duality plays an essential part in this (generally) nonconvex duality result. According to the choice of the data, the duality formula we obtain covers various situations in nonconvex and convex optimization.
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© 1998 Kluwer Academic Publishers. Printed in the Netherlands
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Lemaire, B., Volle, M. (1998). Duality in DC Programming. In: Crouzeix, JP., Martinez-Legaz, JE., Volle, M. (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Nonconvex Optimization and Its Applications, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3341-8_15
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DOI: https://doi.org/10.1007/978-1-4613-3341-8_15
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