Strong global convergence properties of algorithms for nonlinear symmetric cone programming

R. Andreani (), G. Haeser (), A. Ramos (), D. O. Santos (), L. D. Secchin () and A. Serranoni ()
Additional contact information
R. Andreani: University of Campinas
G. Haeser: University of São Paulo
A. Ramos: Universidad de Tarapacá
D. O. Santos: Federal University of São Paulo
L. D. Secchin: Federal University of Espírito Santo
A. Serranoni: University of São Paulo

Computational Optimization and Applications, 2025, vol. 91, issue 2, No 3, 397-421

Abstract: Abstract Sequential optimality conditions have played a major role in establishing strong global convergence properties of numerical algorithms for many classes of optimization problems. In particular, the way complementarity is handled defines different optimality conditions and is fundamental to achieving a strong condition. Typically, one uses the inner product structure to measure complementarity, which provides a general approach to conic optimization problems, even in the infinite-dimensional case. In this paper we exploit the Jordan algebraic structure of symmetric cones to measure complementarity, resulting in a stronger sequential optimality condition related to the well-known complementary approximate Karush-Kuhn-Tucker conditions in standard nonlinear programming. Our results improve some known results in the setting of semidefinite programming and second-order cone programming in a unified framework. In particular, we obtain global convergence that are stronger than those known for augmented Lagrangian and interior point methods for general symmetric cones.

Keywords: Nonlinear symmetric cone optimization; Sequential optimality conditions; Numerical algorithms; Global convergence (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-024-00642-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:91:y:2025:i:2:d:10.1007_s10589-024-00642-z

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-024-00642-z

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().