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Found 3 papers, 1 papers with code
Majorizing Measures for the Optimizer
In this paper, we return to majorizing measures as a primary object of study, and give a viewpoint that we think is natural and clarifying from an optimization perspective.
Gaussian Processes
Probability
Data Structures and Algorithms
Optimization and Control
60G15, 68Q87
G.3
On the Integrality Gap of Binary Integer Programs with Gaussian Data
For a binary integer program (IP) ${\rm max} ~ c^\mathsf{T} x, Ax \leq b, x \in \{0, 1\}^n$, where $A \in \mathbb{R}^{m \times n}$ and $c \in \mathbb{R}^n$ have independent Gaussian entries and the right-hand side $b \in \mathbb{R}^m$ satisfies that its negative coordinates have $\ell_2$ norm at most $n/10$, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by $\operatorname{poly}(m)(\log n)^2 / n$ with probability at least $1-2/n^7-2^{-\operatorname{poly}(m)}$.
Optimization and Control Data Structures and Algorithms
The Gram-Schmidt Walk: A Cure for the Banaszczyk Blues
An important result in discrepancy due to Banaszczyk states that for any set of $n$ vectors in $\mathbb{R}^m$ of $\ell_2$ norm at most $1$ and any convex body $K$ in $\mathbb{R}^m$ of Gaussian measure at least half, there exists a $\pm 1$ combination of these vectors which lies in $5K$.
Data Structures and Algorithms Discrete Mathematics
