The equivalence of optimal perspective formulation and Shor's SDP for quadratic programs with indicator variables

TL;DR

This paper demonstrates that the optimal perspective reformulation and Shor's SDP relaxation are equivalent in strength for quadratic programs with indicator variables, unifying two prominent relaxation techniques.

Contribution

It proves the equivalence between the optimal perspective formulation and Shor's SDP for a class of quadratic programs with indicator variables.

Findings

The two formulations are mathematically equivalent.

This unification simplifies the analysis of relaxation methods.

Potential implications for solving quadratic programs more efficiently.

Abstract

In this paper, we compare the strength of the optimal perspective reformulation and Shor's SDP relaxation. We prove these two formulations are equivalent for quadratic optimization problems with indicator variables.