- Maximizing a class of submodular utility functions with constraints Jiajin Yu(jiajinyugatech.edu) Shabbir Ahmed(sahmedisye.gatech.edu) Abstract: Motivated by stochastic 0-1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: $P = \cset{(w,x)\in \reals \times \set{0,1}^N}{w \leq f(a'x + d), b'x \leq B}$ where $N$ is a positive integer, $f:\reals \mapsto \reals$ is a concave function, $a, b \in \reals^N$ are nonnegative vectors, $d$ is a real number and $B$ is a positive real number. We propose a family of inequalities for the convex hull of $P$ by exploiting submodularity of the function $f(a'x + d)$ over $\{0,1\}^N$ and the knapsack constraint $b'x \leq B$. Computational effectiveness of the proposed inequalities within a branch-and-cut framework is illustrated using instances of an expected utility capital budgeting problem. Keywords: Submodularity, cutting planes, lifting, mixed integer nonlinear programming, branch-and-cut Category 1: Integer Programming (0-1 Programming ) Category 2: Integer Programming (Cutting Plane Approaches ) Category 3: Stochastic Programming Citation: Submitted for publication, December 2014. Download: [PDF]Entry Submitted: 12/30/2014Entry Accepted: 12/30/2014Entry Last Modified: 12/30/2014Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.