Convexy - convex enveopes

Asked May 20 '17 at 08:22

Active May 20 '17 at 08:29

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I got stuck with one task, please any help.

Given the function $f (x_1,x_2,x_3) = ax_1x_2 + bx_1x_3$, $x_1,x_2,x_3\in[L,U], \,L,U\in\mathbb{R}$. Does convex envelope of $f$ ever strictly dominate the sum of conv. envelopes of each terms, i.e., $\mathrm{convenv}(ax_1x_2) + \mathrm{convenv}(bx_1x_3) $?

edited May 20 '17 at 08:29

asked May 20 '17 at 08:22

user207950

What do the [] brackets mean here? – Veliko May 20 '17 at 08:25
Closed interval from where the values $x_1,x_2,x_3$ are chosen. – user207950 May 20 '17 at 08:31

Convexy - convex enveopes

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