6 papers
Disjunctive Submodular Functions: Envelopes and Applications to Inventory and 0-1 Quadratic Optimization
Zhongqi Wu, Taotao He, Mohit Tawarmalani
This paper considers convex envelopes of disjunctive submodular functions---functions that are lattice family submodular over faces of a hypercube---and constructs the first strong…
Axis-Aligned Relaxations for Mixed-Integer Nonlinear Programming
Haisheng Zhu, Taotao He, Mohit Tawarmalani
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations b…
Discreteness to Convexity: Promotion Planning via Simplotope Triangulation
Taotao He, Mohit Tawarmalani
Price promotion optimization is a computationally challenging problem central to supermarket operations, requiring simultaneous pricing decisions across multiple products and perio…
Convexification Techniques for Fractional Programs
Taotao He, Siyue Liu, Mohit Tawarmalani
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number o…
MIP Relaxations in Factorable Programming
Taotao He, Mohit Tawarmalani
In this paper, we develop new discrete relaxations for nonlinear expressions in factorable programming. We utilize specialized convexification results as well as composite relaxati…
Extracting structure from functional expressions for continuous and discrete relaxations of MINLP
Taotao He, Mohit Tawarmalani
In this paper, we develop new continuous and discrete relaxations for nonlinear expressions in an MINLP. In contrast to factorable programming, our techniques utilize the inner-fun…