13 problems

Consider mixed-integer bilevel linear optimization instances classified by their objective alignment, and compare cut-generation performance with and without mixed-integer linear p…

Consider mixed-integer bilevel linear optimization instances with an objective-alignment parameter, and let the cut-generation failure rate denote the proportion of attempted inter…

Mixed-integer bilevel linear optimization problems may use intersection cuts (ICs), including integer disjunctive intersection cuts and integer split intersection cuts, together wi…

Conjecture on the speedup difference. These two features are the reasons for the smaller speedup in the exact setting.

The NFP-CM-VS and NFP-CM-VS2 formulations are mixed-integer programming models for irregular strip packing, with NFP-CM-VS2 being more compact than NFP-CM-VS. NFP-CM-VS tightening…

The face dimension of a cut is the dimension of the face it induces in the feasible region of a mixed-integer linear program; empirically, face dimensions are often concentrated ne…

An MVB instance consists of variables $(l_i,r_i)_{1\leq i\leq n}$, with recurrence … Its variable ratios are denoted by $\varphi_i$. The MVB conjecture. For each instance of MVB, t…

CPLEX structure-exploitation conjecture. We conjecture that this favorable outcome can be attributed to CPLEX's capability of identifying the particular structure of this formulati…

Existence conjecture. There exist conic mixed-integer programs whose subadditive dual is feasible but whose conic dual of the continuous relaxation is infeasible.

Let $\mathcal{A}\in T_{m,n}$ be a diagonal tensor, let $q\in\mathbb{R}^n$, and consider the tensor complementarity problem $\operatorname{TCP}(\mathcal{A},q)$: find…

Let $A$ be the constraint matrix, let $\Delta$ be the largest absolute value of any determinant of a square submatrix of $A$, and let $I,J\subseteq[n]$ index the variables required…

Let $G=(V,E)$ be the underlying graph, and let its line graph have pathwidth bounded by $k\in\mathcal{O}(\log(|V|+|E|))$. The pre-disaster planning reformulation conjecture. The pr…

Let $C = \{(x,y) \in \mathbb R^p \times \mathbb R^q: Px + Qy \leq d\}$, where $P \in \mathbb R^{m \times p}$ and $Q \in \mathbb R^{m \times q}$. Its mixed integer hull is … For eve…