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The paper investigates the problem of fitting protein complexes into electrondensity maps. They are represented by high-resolution cryoEM density mapsconverted into overlapping matrices and partly show a structure of a complex.The general purpose is to define positions of all proteins inside it. Thisproblem is known to be NP-hard, since it lays in the field of combinatorialoptimization over a set of discrete states of the complex. We introducequadratic programming approaches to the problem. To find an approximatesolution, we convert a density map into an overlapping matrix, which isgenerally indefinite. Since the matrix is indefinite, the optimization problemfor the corresponding quadratic form is non-convex. To treat non-convexity ofthe optimization problem, we use different convex relaxations to find which setof proteins minimizes the quadratic form best.

Quadratic Programming Approach to Fit Protein Complexes into Electron Density Maps