Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Asymptotic Cones Of Quadratically Defined Sets And Their Applications To Qcqps, Alexander Joyce
Asymptotic Cones Of Quadratically Defined Sets And Their Applications To Qcqps, Alexander Joyce
All Dissertations
Quadratically constrained quadratic programs (QCQPs) are a set of optimization problems defined by a quadratic objective function and quadratic constraints. QCQPs cover a diverse set of problems, but the nonconvexity and unboundedness of quadratic constraints lead to difficulties in globally solving a QCQP. This thesis covers properties of unbounded quadratic constraints via a description of the asymptotic cone of a set defined by a single quadratic constraint. A description of the asymptotic cone is provided, including properties such as retractiveness and horizon directions.
Using the characterization of the asymptotic cone, we generalize existing results for bounded quadratically defined regions with …