English

Finding global solutions for a class of possibly nonconvex QCQP problems through the S-lemma

Optimization and Control 2022-06-02 v1

Abstract

In this paper we provide necessary and sufficient (KKT) conditions for global optimality for a new class of possibly nonconvex quadratically constrained quadratic programming (QCQP) problems, denoted by S-QCQP. The class consists of QCQP problems where the matrices of the quadratic components are formed by a scalar times the identity matrix. Our result relies on a generalized version of the S-Lemma, stated in the context of general QCQP problems. Moreover, we prove the exactness of the SDP and the SOCP relaxations for S-QCQP.

Keywords

Cite

@article{arxiv.2206.00618,
  title  = {Finding global solutions for a class of possibly nonconvex QCQP problems through the S-lemma},
  author = {Ewa M. Bednarczuk and Giovanni Bruccola},
  journal= {arXiv preprint arXiv:2206.00618},
  year   = {2022}
}