Suppose I have the problem $$ \text{minimize } f_0(x)\\ \text{subject to } tf_1(x) \leq r $$ with variables $t,x \in \mathbb{R}$ and $f_0, f_1$ are convex. The constraint is not convex, so I was thinking using a variable $y = t*x$ then I can write the constraint as $tf_1(y/t) \leq r$ which is now convex. But the problem then is that the objective is no longer convex, since it is $f_0(y/t)$.
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What is the question? Why is the transformed constraint convex? – copper.hat Mar 12 '16 at 19:32
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Try setting $y=1/t$ instead? – Mar 12 '16 at 19:32
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Am I still using perspective function then? I'm not sure what $y$ maps to. – user90593 Mar 12 '16 at 19:40
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Not all problems can be transformed into a convex problem... – copper.hat Mar 12 '16 at 19:44
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But this one is supposed to be so. – user90593 Mar 12 '16 at 19:45
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Then you need to give more information. If $f_1$ convex? What properties does $f_0$ have??? – copper.hat Mar 12 '16 at 19:46
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Both of them are convex. – user90593 Mar 12 '16 at 20:17