FURTHER DEVELOPMENT IN CONVEX CONIC REFORMULATION OF GEOMETRIC NONCONVEX CONIC OPTIMIZATION PROBLEMS

Naohiko Arima, Sunyoung Kim, Masakazu Kojima

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A geometric nonconvex conic optimization problem (COP) was recently proposed by Kim, Kojima, and Toh (SIAM J. Optim., 30 (2020), pp. 1251̶1273) as a unified framework for convex conic reformulation of a class of quadratic optimization problems and polynomial optimization problems. The nonconvex COP minimizes a linear function over the intersection of a nonconvex cone K, a convex subcone J of the convex hull coK of K, and an affine hyperplane with a normal vector H. Under the assumption co(K ∩ J) = J, the original nonconvex COP in their paper was shown to be equivalently formulated as a convex conic program by replacing the constraint set with the intersection of J and the affine hyperplane. This paper further studies the key assumption co(K ∩ J) = J in their framework and provides three sets of necessary-sufficient conditions for the assumption. Based on the conditions, we propose a new wide class of quadratically constrained quadratic programs with multiple nonconvex equality and inequality constraints, which can be solved exactly by their semidefinite relaxation.

Original languageEnglish
Pages (from-to)3194-3211
Number of pages18
JournalSIAM Journal on Optimization
Volume34
Issue number4
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

  • convex conic reformulation
  • exact semidefinite relaxation
  • geometric conic optimization problem
  • polynomial optimization problem
  • positive semidefinite cone
  • quadratically constrained quadratic program

Fingerprint

Dive into the research topics of 'FURTHER DEVELOPMENT IN CONVEX CONIC REFORMULATION OF GEOMETRIC NONCONVEX CONIC OPTIMIZATION PROBLEMS'. Together they form a unique fingerprint.

Cite this