Abstract
Abstract We introduce a computer program PENNON for the solution of problems of convex Nonlinear and Semidefinite Programming (NLP-SDP). The algorithm used in PENNON is a generalized version of the Augmented Lagrangian method, originally introduced by Ben-Tal and Zibulevsky for convex NLP problems. We present generalization of this algorithm to convex NLP-SDP problems, as implemented in PENNON and details of its implementation. The code can also solve second-order conic programming (SOCP) problems, as well as problems with a mixture of SDP, SOCP and NLP constraints. Results of extensive numerical tests and comparison with other optimization codes are presented. The test examples show that PENNON is particularly suitable for large sparse problems. Keywords: Convex ProgrammingSemidefinite ProgrammingLarge-scale Problems
Keywords
Semidefinite programmingGeneralizationNonlinear programmingConvex optimizationMathematical optimizationRegular polygonConic optimizationComputer scienceCode (set theory)Second-order cone programmingNonlinear systemMathematicsAlgorithmConvex analysisProgramming language
Affiliated Institutions
Related Publications
Robust Solutions to Least-Squares Problems with Uncertain Data
We consider least-squares problems where the coefficient matrices A, b are unknown but bounded. We minimize the worst-case residual error using (convex) second-order cone progra...
SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
This software package is a MATLAB implementation of infeasible path-following algorithms for solving standard semidefinite programs (SDP). Mehrotra-type predictor-corrector vari...
SDPT3 -- A Matlab Software Package for Semidefinite Programming
This software package is a Matlab implementation of infeasible path-following algorithms for solving standard semidefinite programs (SDP). Mehrotra-type predictor-corrector vari...
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and co...
Self-Scaled Barriers and Interior-Point Methods for Convex Programming
This paper provides a theoretical foundation for efficient interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated ba...
Publication Info
- Year
- 2003
- Type
- article
- Volume
- 18
- Issue
- 3
- Pages
- 317-333
- Citations
- 293
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
293
OpenAlex
Cite This
Michal Kočvara,
Michael Stingl
(2003).
PENNON: A code for convex nonlinear and semidefinite programming.
Optimization methods & software
, 18
(3)
, 317-333.
https://doi.org/10.1080/1055678031000098773
Identifiers
- DOI
- 10.1080/1055678031000098773