Speeding up computation of the max/min of a set of gaussians for statistical timing analysis and optimization

The increasing significance of variability in modern sub-micron manufacturing process has led to the development and use of statistical techniques for chip timing analysis and optimization. Statistical timing involves fundamental operations like ...

We consider the robust (or min-max) optimization problem $$J^*:=\max_{\mathbf{y}\in{\Omega}}\min_{\mathbf{x}}\{f(\mathbf{x},\mathbf{y}): (\mathbf{x},\mathbf{y})\in\mathbf{\Delta}\}$$ where f is a polynomial and $${\mathbf{\Delta}\subset\mathbb{R}^n\...

We show that for any lattice $\mathcal{L} \subseteq \mathbb{R}^n$ and vectors $\mathbf{x}, \mathbf{y} \in \mathbb{R}^n$, $\rho(\mathcal{L} + \mathbf{x})^2 \rho(\mathcal{L} + \mathbf{y})^2 \leq \rho(\mathcal{L})^2 \rho(\mathcal{L} + \mathbf{x} + \mathbf{y}) \...