Fractional 0–1 programming and submodularity

• Published in: Journal of global optimization Vol. 84; no. 1; pp. 77 - 93
• Main Authors: Han, Shaoning, Gómez, Andrés, Prokopyev, Oleg A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Approximation; Combinatorial analysis; Computer Science; Greedy algorithms; Industrial locations; Integer programming; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Real Functions; Facility location; Fractional 0–1 programming; Single ratio; Hyperbolic 0–1 programming; Assortment optimization; Greedy algorithm; Multiple ratios; Submodularity

In this note we study multiple-ratio fractional 0–1 programs, a broad class of NP -hard combinatorial optimization problems. In particular, under some relatively mild assumptions we provide a complete characterization of the conditions, which ensure that a single-ratio function is submodular. Then w...