Combinatorial Optimization is an area of mathematics that thrives from a continual influx of new questions and problems from practice. Attacking these problems has required the development and combination of ideas and techniques from different mathematical areas including graph theory, matroids and combinatorics, convex and nonlinear optimization, discrete and convex geometry, algebraic and topological methods. We continued a tradition of triannual Oberwolfach workshops, bringing together the best international researchers with younger talent to discover new connections with a particular emphasis on emerging breakthrough areas.