Abstract
Exercise 1: (i) First, observe that \(p_{C}(\theta )=\inf \{\lambda \ge 0:\theta \in \lambda C\}=0\). To check that \(p_{C}\) is positively homogeneous on \({\text {dom}}\,p_{C}\), we fix \(x\in {\text {dom}}\,p_{C}\) and \(\alpha \ge 0.\) If \(\alpha =0,\) then \(p_{C}(0x)=p_{C}(\theta )=0=0p_{C}(x).\) If \(\alpha >0,\) then.
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Correa, R., Hantoute, A., López, M.A. (2023). Exercises - Solutions. In: Fundamentals of Convex Analysis and Optimization. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-29551-5_9
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DOI: https://doi.org/10.1007/978-3-031-29551-5_9
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