English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider quadratic optimization in variables $(x,y)$ where $0\le x\le y$,and $y\in\{0,1\}^n$. Such binary $y$ are commonly refered to as "indicator" or"switching" variables and occur commonly in applications. One approach to suchproblems is based on representing or approximating the convex hull of the set$\{ (x,xx^T, yy^T) : 0\le x\le y\in\{0,1\}^n\}$. A representation for the case$n=1$ is known and has been widely used. We give an exact representation forthe case $n=2$ by starting with a disjunctive representation for the convexhull and then eliminating auxilliary variables and constraints that do notchange the projection onto the original variables. An alternative derivationfor this representation leads to an appealing conjecture for a simplifiedrepresentation of the convex hull for $n=2$ when the product term $y_1y_2$ isignored.

Quadratic Optimization with Switching Variables: The Convex Hull for $n = 2$