23. Shor convexity, min-max QCQPs and application to min-max regret of nonconvex QPs
Invited abstract in session TD-2: Conic and polynomial optimization, stream Conic and polynomial optimization.
Thursday, 14:45 - 16:15Room: C 103
Authors (first author is the speaker)
| 1. | Immanuel Bomze
|
| Dept. of Statistics and OR, University of Vienna | |
| 2. | Paula Amaral
|
| Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa |
Abstract
Under (finitely many) uncertain scenarios, min-max regret for (possibly nonconvex) Standard QPs can be reduced to a min-max QCQP.
En route to narrowing the gap between powerful conic lower bounds and efficient upper bounds, i.e. good feasible values, we will study
the apparently novel notion of *Shor convexity* (not to be confused with the well-known notion of Schur convexity) suggested by lifting techniques,
and discuss possibilities to use bundle methods for tightening upper bounds. A generalization of the famous Jensen's inequality will be proved as well.
Keywords
- Conic and semidefinite optimization
- Convex and non-smooth optimization
- Linear and nonlinear optimization
Status: accepted
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