Quadratic problems with two quadratic constraints: Convex quadratic relaxation and strong lagrangian duality
Abstract
In this paper, we study a nonconvex quadratic minimization problem with two quadratic constraints, one of which being convex. We introduce two convex quadratic relaxations (CQRs) and discuss cases, where the problem is equivalent to exactly one of the CQRs. Particularly, we show that the global optimal solution can be recovered from an optimal solution of the CQRs. Through this equivalence, we introduce new conditions under which the problem enjoys strong Lagrangian duality, generalizing the recent condition in the literature. Finally, under the new conditions, we present necessary and sufficient conditions for global optimality of the problem. EDP Sciences, ROADEF, SMAI 2021.
Collections
- Mathematics, Statistics & Physics [738 items ]
Related items
Showing items related by title, author, creator and subject.
-
On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints
( Springer , 2022 , Article)In this paper, we study the minimization of an indefinite quadratic function over theintersection of balls and linear inequality constraints (QOBL). Using the hyperplanesinduced by the intersection of each pair of balls, ... -
A hybrid TDMA-MAC cooperative relaying scheme: Stability and delay analysis
( Institute of Electrical and Electronics Engineers Inc. , 2016 , Conference Paper)We consider a cooperative relaying system with any number of source terminals, one shared relay, and a common destination. We assume a slotted time division multiple access (TDMA) framework in which each source terminal ... -
Time-Frequency Characterization of Tri-Axial Accelerometer Data for Fetal Movement Detection
( IEEE , 2011 , Conference Paper)Monitoring fetal wellbeing is a significant problem in modern obstetrics. Clinicians have become increasingly aware of the link between fetal activity and its well-being. Using data acquired by accelerometry sensors, we ...
