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We assume that $a,b \in \mathbb{C}^{N\times1},b^Hb\leq\epsilon^2$. Is the function $Q(b)=a^Hb+b^Ha$ convex,concave? In other words, which of the following problems is feasible?

$\min\ \ a^Hb+b^Ha \\ s.t.\ \ \ b^Hb\leq\epsilon^2$

or

$\max\ \ a^Hb+b^Ha \\ s.t.\ \ \ b^Hb\leq\epsilon^2$

begforopt
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    Do I overlook something. Your function is real-linear, hence convex and concave, as $$ Q((1-\lambda)b_1 + \lambda b_2) = (1-\lambda)Q(b_1) + \lambda Q(b_2)$$ for $\lambda \in [0,1]$. – martini Oct 01 '13 at 11:14
  • Thanks for your reply, martini. I am just a beginner. – begforopt Oct 01 '13 at 11:41

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