Conic Programming Reformulations and Relaxations for Quadratically Constrained and Quadratic Programs
Abstract
Quadratically Constrained Quadratic Programming (QCQP) isa fundamental class of problems in optimization theory and practice. It nat-urally arises in theoretical research such as polynomial optimization, trust-region methods for nonlinear programming, robust optimization and Booleanoptimization. QCQP models are also widely employed in real-life applicationssuch as power system optimization, facility location problems, transceiverdesign problems. Despite its extensive applications, a QCQP problem is NP-hard in general. The objective of this research project is threefold. The rstobjective is to derive new tighter valid inequalities for QCQP with specialstructure. Strengthened RLT constraints will be studied and applied to vari-ous conic relaxations. The second objective is to explore specially structuredQCQP and derive tractable conic programming reformulations. Along theway, hidden convexity and duality theory of the problems will be discussed.The third objective is to develop conic approximation for a more general classof QCQP. The conic approximation will lead to tight tractable relaxations,which will play an important role in solving QCQP eciently.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 29, 2020
- Source ID
- N000142012154
Entities
People
- Boshi Yang
Organizations
- Clemson University
- Office of Naval Research
- United States Navy