Sums of convex functions strictly convex in one variable

Question

Let $f_i:\mathbb{R}^n\to\mathbb{R}$, $i=1,2,\ldots,n$ be twice continuously differentiable, convex functions in $x = (x_1,x_2,\ldots,x_n)$. Let each $f_i$ be strictly convex in $x_i$. Is the function $$g(x) = \sum_{i=1}^n f_i(x)$$ strictly convex in $x$?

user7530 · Accepted Answer · 2014-04-04T01:44:20.513

5

No. Consider $f_1 = f_2 = x^2+2xy+y^2.$

edited Apr 04 '14 at 01:44

answered Apr 04 '14 at 01:33

user7530

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Sums of convex functions strictly convex in one variable

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