AbstractThis paper presents a generalization, calledpolaroid, of the concept ofpolarsetsA list of properties satisfied by polaroids is established indicating that the new concept nay be fruitfully used in an area of non‐convex (called here polar) programming as well as in integer programming, by means of polaroid cuts; this class of new cuts contains the ones defined by Tuy for concave programming (a special case of polar programming) and by Balas integer programming; it furthermore provides for new degrees of freedom in the construction of algorithms in the above‐mentioned areas of mathematical programm