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In this work we study convex relaxations of quadratic optimisation problemsover permutation matrices. While existing semidefinite programming approachescan achieve remarkably tight relaxations, they have the strong disadvantagethat they lift the original $n {\times} n$-dimensional variable to an $n^2{\times} n^2$-dimensional variable, which limits their practical applicability.In contrast, here we present a lifting-free convex relaxation that is provablyat least as tight as existing (lifting-free) convex relaxations. We demonstrateexperimentally that our approach is superior to existing convex and non-convexmethods for various problems, including image arrangement and multi-graphmatching.

DS*: Tighter Lifting-Free Convex Relaxations for Quadratic Matching Problems