# DCP constraint version of $a^2 + b^2 \leq c^2$

I have a second order cone constraint

$$a^2 + b^2 \leq c^2$$ where $$c_{min} <= c <= c_{max}$$ $$a^2tan(z_{min}) <= b <=a^2tan(z_{max})$$ While $\ z_{min}<= 0$, $\ c_{min}, c_{max}, z_{max} >= 0$ .

This is a relaxation of an equality constraint $a^2 + b^2 = c^2$. How can I express the constraint in a form fitting disciplined convex programming (DCP) inequality requirements?

This is very much a "learning" question for me, as I'm still in the process of learning about convex optimization, DCP, and SOCP. Additional details are appreciated!

• Constraint in what variables? – Rodrigo de Azevedo Feb 28 '18 at 6:59
• @Masacroso: I would think this question about convex-optimization is very well suited for MathStackExchange. – MrYouMath Feb 28 '18 at 8:48
• @Masacroso it is certainly not a stackoverflow question. – Michael Grant Feb 28 '18 at 16:22
• Is $c$ known to be nonnegative? If not this isn't convex. If so, it's equivalent to $\|[a~b]\|_2 \leq c$. – Michael Grant Feb 28 '18 at 16:23
• Ah ha! Yes, $\ c$ is known to be non-negative. I forgot to mention additional constraints on a, b, c (updating jn the question). $\ norm(a+b,2) <= c$ makes a lot of sense! I thought it would be simple just not that simple :) Thank you – Jonny Hyman Feb 28 '18 at 16:32