2022/06/01 by Ewa M. Bednarczuk, Giovanni Bruccola, Bednarczuk, Ewa M. +1
Mathematics · Computer Science · Engineering · #Advanced Optimization Algorithms Research #Optimization and Variational Analysis #Advanced Control Systems Optimization
paper · pdf · doi:10.48550/arxiv.2206.00618
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.