I know that log_sum_exp form is convex.
Is the following sum_log_exp form convex?
$$ \sum_{i=1}^n \log_2 (a\, 2^{x_i} + b) $$ where constants a,b >= 0 and $x_i \geq 0$
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The question is badly stated. I suppose you have a finite sum and you are asking for convexity in the variable $x_1,x_2,...,x_n$ You have not specified the domain. In the case n=1 the function is convex in some part of the real line and concave in others. – Kavi Rama Murthy Jan 04 '18 at 05:54
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Hi Basem Elhalawany and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? – Taroccoesbrocco Jan 04 '18 at 07:03
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@KaviRamaMurthy thank you for your reply. I updated the question. I tried to tried plot this term in the domain ($x_i \geq 0$) for n=1,2 and the result was a straight line. That is why I am asking if the function is affine in this domain – Basem Elhalawany Jan 05 '18 at 09:09