A Note on Generalizing Power Bounds for Physical Design

TL;DR

This paper introduces a method to derive nonconvex quadratic inequalities from physics equations to establish bounds in physical design problems, facilitating analysis of quadratic objectives with practical verification.

Contribution

It presents a novel approach to generalize power bounds in physical design by linking physics equations with quadratic inequalities under verifiable conditions.

Findings

Quadratic inequalities can be constructed from physics equations.

These inequalities provide bounds for quadratic and ratio-of-quadratics objectives.

The equivalence holds under a practical, verifiable condition.

Abstract

In this note we show how to construct a number of nonconvex quadratic inequalities for a variety of physics equations appearing in physical design problems. These nonconvex quadratic inequalities can then be used to construct bounds on physical design problems where the objective is a quadratic or a ratio of quadratics. We show that the quadratic inequalities and the original physics equations are equivalent under a technical condition that holds in many practical cases which is easy to computationally (and, in some cases, manually) verify.