compactness

Political districting to minimize cut edges

  • Austin Buchanan
  • Hamidreza Validi
    • Categories Combinatorial Optimization, Integer Programming, Network Optimization Tags , , , , , , , ,

    When constructing political districting plans, prominent criteria include population balance, contiguity, and compactness. The compactness of a districting plan, which is often judged by the “eyeball test,” has been quantified in many ways, e.g., Length-Width, Polsby-Popper, and Moment-of-Inertia. This paper considers the number of cut edges, which has recently gained traction in the redistricting literature … Read more

    Tangencies and Polynomial Optimization

  • Tiên-So'n Pham
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory Tags , , , , , , , , ,

    Given a polynomial function $f \colon \mathbb{R}^n \rightarrow \mathbb{R}$ and a unbounded basic closed semi-algebraic set $S \subset \mathbb{R}^n,$ in this paper we show that the conditions listed below are characterized exactly in terms of the so-called {\em tangency variety} of $f$ on $S$: (i) The $f$ is bounded from below on $S;$ (ii) The … Read more