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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider in this paper a class of semi-continuous quadratic programmingproblems which arises in many real-world applications such as productionplanning, portfolio selection and subset selection in regression. We propose alift-and-convexification approach to derive an equivalent reformulation of theoriginal problem. This lift-and-convexification approach lifts the quadraticterm involving $x$ only in the original objective function $f(x,y)$ to aquadratic function of both $x$ and $y$ and convexifies this equivalentobjective function. While the continuous relaxation of our new reformulationattains the same tight bound as achieved by the continuous relaxation of thewell known perspective reformulation, the new reformulation also retains thelinearly constrained quadratic programming structure of the originalmix-integer problem. This prominent feature improves the performance ofbranch-and-bound algorithms by providing the same tightness at the root node asthe state-of-the-art perspective reformulation and offering much fasterprocessing time at children nodes. We further combine thelift-and-convexification approach and the quadratic convex reformulationapproach in the literature to form an even tighter reformulation. Promisingresults from our computational tests in both portfolio selection and subsetselection problems numerically verify the benefits from these theoreticalfeatures of our new reformulations.

Tight MIQP Reformulations for Semi-Continuous Quadratic Programming: Lift-and-Convexification Approach