Galaxy Redshifts from Discrete Optimization of Correlation Functions
  We propose a new method of constraining the redshifts of individual
extragalactic sources based on celestial coordinates and their ensemble
statistics. Techniques from integer linear programming are utilized to optimize
simultaneously for the angular two-point cross- and autocorrelation functions.
Our novel formalism introduced here not only transforms the otherwise
hopelessly expensive, brute-force combinatorial search into a linear system
with integer constraints but also is readily implementable in off-the-shelf
solvers. We adopt Gurobi, a commercial optimization solver, and use Python to
build the cost function dynamically. The preliminary results on simulated data
show potential for future applications to sky surveys by complementing and
enhancing photometric redshift estimators. Our approach is the first
application of integer linear programming to astronomical analysis.
