Abstract
Two generations of mathematicians have labored to extend the machinery of differential calculus to convex functions. For many purposes it is convenient to generalize the definition of a convex function \(f(\boldsymbol{x})\) to include the possibility that \(f(\boldsymbol{x}) = \infty \). This maneuver has the advantage of allowing one to enlarge the domain of a convex function \(f(\boldsymbol{x})\) defined on a convex set C ;⊂ ;R n to all of R n by the simple device of setting \(f(\boldsymbol{x}) = \infty \) for \(\boldsymbol{x}\not\in C\).
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Lange, K. (2013). Convex Calculus. In: Optimization. Springer Texts in Statistics, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5838-8_14
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DOI: https://doi.org/10.1007/978-1-4614-5838-8_14
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