Integer and combinatorial optimization
Integer and combinatorial optimization
Maximizing classes of two-parameter objectives over matroids
Mathematics of Operations Research
On the supermodular knapsack problem
Mathematical Programming: Series A and B
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Introduction to algorithms
Lifted Cover Inequalities for 0-1 Integer Programs: Computation
INFORMS Journal on Computing
Exact Solution of the Quadratic Knapsack Problem
INFORMS Journal on Computing
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
SIAM Journal on Optimization
Cuts for mixed 0-1 conic programming
Mathematical Programming: Series A and B
Polymatroids and mean-risk minimization in discrete optimization
Operations Research Letters
Operations Research Letters
Robust solutions of uncertain linear programs
Operations Research Letters
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
The Chvátal-Gomory Closure of a Strictly Convex Body
Mathematics of Operations Research
The chvátal-gomory closure of an ellipsoid is a polyhedron
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Facial structure and representation of integer hulls of convex sets
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Recursive central rounding for mixed integer programs
Computers and Operations Research
| Hi-index | 0.00 |
The submodular knapsack set is the discrete lower level set of a submodular function. The modular case reduces to the classical linear 0-1 knapsack set. One motivation for studying the submodular knapsack polytope is to address 0-1 programming problems with uncertain coefficients. Under various assumptions, a probabilistic constraint on 0-1 variables can be modeled as a submodular knapsack set. In this paper we describe cover inequalities for the submodular knapsack set and investigate their lifting problem. Each lifting problem is itself an optimization problem over a submodular knapsack set. We give sequence-independent upper and lower bounds on the valid lifting coefficients and show that whereas the upper bound can be computed in polynomial time, the lower bound problem is NP-hard. Furthermore, we present polynomial algorithms based on parametric linear programming and computational results for the conic quadratic 0-1 knapsack case.