# Numerical Methods for minimizing a Non-Differentiable Convex Function of Several Variables

I have a multi-variable convex continuous function which is not differentiable. I am interested to know about different numerical techniques, possibly also references to them, used for this.

Read the following only if you want to know the function I want to minimize (this is a concave function, I want to maximize it, which is equivalent to minimizing its negative) . \begin{align} f(t_1,t_2)=\min_{u^Tu=1,u\in \mathbb{R}^{N}}u^T(A_0+t_1A_1+t_2A_2)u \end{align} $A_0,A_1,A_2$ are all $N \times N$ real symmetric matrices. Actually $f(t_1,t_2)$ is the lowest eigenvalue of matrix $A_0+t_1A_1+t_2A_2$ for a given $t_1,t_2$. I know this can be solved by semi-definite programming.

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