Chapter Ten Mixed Smooth-Convex Problems · What are the necessary conditions for problems that are partly smooth and partly convex? But definite concrete problems were first conquered in their undi- vided complexity, singlehanded by brute force, so to speak. Only afterwards the axiomaticians came along and stated: Instead of breaking in the door with all your might and bruising your hands, you should have constructed such and such a key of skills, and by it you would have been able to open the door quite smoothly. But they can construct the key only because they are able, after the breaking in was successful, to study the lock from within and without. Before you generalize, formalize, and axiomatize, there must be mathematical substance.