16 problems

Let $C \subseteq \mathbb R^n \times \mathbb R^d$ be a compact, convex set and let $S=C\cap(\mathbb Z^n\times\mathbb R^d)$. For $S$, define its mixed-integer volume by … with counti…

Mixed-integer oracle lower-bound conjecture. Under these assumptions, at least

Let $\mathcal{L}$ denote the continuous Benders relaxation, and let $\textsc{BendersSeq}$ and $\textsc{BendersBnB}$ denote the sequential and branch-and-Benders implementations, re…

Runtime conjecture. The runtime of MINLP solvers increases for more redundant ANN models and decreases for less redundant ANN models.

Let the RGUP constraints be the constraints presented in Appendix. Unbounded-relaxation conjecture. The result of Lemma holds for these RGUP constraints. The observed unbounded roo…

Let the EFL constraints be the constraints stated in Appendix. Unbounded-relaxation conjecture. The result of Lemma holds for these EFL constraints. This would explain the unbounde…

Let $u(n,d,R,\rho,M,\mathcal{G})$ denote the worst-case information complexity of a query strategy under the full-information first-order oracle based on a first-order chart…

Let $n$ be the number of integer variables, let $d$ be the continuous dimension, and let $M$, $R$, $\rho$, and $\varepsilon$ be the problem parameters. A first-order chart…

Let $\ell$ be a lower bound on the information complexity, with respect to a fixed oracle, for a family of continuous, constrained convex optimization instances. Mixed-integer tran…

The matrix $Q$ is the quadratic coefficient matrix, and MILO denotes the mixed-integer linear optimization formulation obtained by reformulating the convex quadratic optimization p…

Outer-approximation conjecture. The formulation might not be particularly challenging to solve via interior point methods, but it might be difficult to construct a good-quality out…

Consider instances of best subset selection for which a mixed-integer optimization solver does not prove optimality within the allotted computation time, and compare their optimali…

Let $X$ be the mixed-integer multilinear feasible region considered in the formulation, and let $\mathfrak{F}^{\lambda}$ be its extended formulation in the variables consisting of…

The experiments compare several formulations for quadratic optimization with indicator variables, including formulations with and without cuts, and consider instances whose size is…

Let $Q^{lb}$ denote the floor-layout disjunction with lower bounds, and let $D^8$ be its eight-branch disjunction encoded by … Let $\operatorname{Em}(Q^{lb},D^8,C^8)$ denote the co…

Let $t$ be the number of treatments and $N$ the number of two-block observations. A design is equireplicate when the numbers of times each treatment is tested are as similar as pos…