Abstract
A functional operation that generates convex functions on ℝn +m from convex functions on ℝn and ℝm originated from the study of the multiplicative potential function. We review some of the properties of this functional operation, including associativity, right distributivity with respect to addition and left distributivity with respect to infimal convolution. We also show how it can be used to build a generalized version of the multiplicative potential function.
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© 2001 Kluwer Academic Publishers
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Maréchal, P. (2001). Generating Convex Functions. In: Hadjisavvas, N., Pardalos, P.M. (eds) Advances in Convex Analysis and Global Optimization. Nonconvex Optimization and Its Applications, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0279-7_21
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DOI: https://doi.org/10.1007/978-1-4613-0279-7_21
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-6942-4
Online ISBN: 978-1-4613-0279-7
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