Pennon: A code for convex nonlinear and semidefinite programming. 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.

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  1. Andreani, Roberto; Haeser, Gabriel; Viana, Daiana S.: Optimality conditions and global convergence for nonlinear semidefinite programming (2020)
  2. Birgin, Ernesto G.; Gómez, Walter; Haeser, Gabriel; Mito, Leonardo M.; Santos, Daiana O.: An augmented Lagrangian algorithm for nonlinear semidefinite programming applied to the covering problem (2020)
  3. Brune, Alexander; Kočvara, Michal: On barrier and modified barrier multigrid methods for three-dimensional topology optimization (2020)
  4. Ghalehnoie, Mohsen; Akbarzadeh-T., Mohammad-R.; Pariz, Naser: Local exponential stabilization for a class of uncertain nonlinear impulsive periodic switched systems with norm-bounded input (2019)
  5. Gronski, Jessica; Ben Sassi, Mohamed-Amin; Becker, Stephen; Sankaranarayanan, Sriram: Template polyhedra and bilinear optimization (2019)
  6. Hafstein, Sigurdur; Kawan, Christoph: Numerical approximation of the data-rate limit for state estimation under communication constraints (2019)
  7. Kanzow, Christian; Steck, Daniel: Improved local convergence results for augmented Lagrangian methods in (C^2)-cone reducible constrained optimization (2019)
  8. Lee, Donghwan; Hu, Jianghai: Sequential parametric convex approximation algorithm for bilinear matrix inequality problem (2019)
  9. Paternain, Santiago; Mokhtari, Aryan; Ribeiro, Alejandro: A Newton-based method for nonconvex optimization with fast evasion of saddle points (2019)
  10. Sánchez, M. D.; Schuverdt, M. L.: A second-order convergence augmented Lagrangian method using non-quadratic penalty functions (2019)
  11. Bacci, Giovanni; Bacci, Giorgio; Larsen, Kim G.; Mardare, Radu: On the metric-based approximate minimization of Markov chains (2018)
  12. Lourenço, Bruno F.; Fukuda, Ellen H.; Fukushima, Masao: Optimality conditions for nonlinear semidefinite programming via squared slack variables (2018)
  13. Shen, Xin; Mitchell, John E.: A penalty method for rank minimization problems in symmetric matrices (2018)
  14. Zhao, Qi; Chen, Zhongwen: An SQP-type method with superlinear convergence for nonlinear semidefinite programming (2018)
  15. Armand, Paul; Omheni, Riadh: A mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization (2017)
  16. Li, Jian-Ling; Yang, Zhen-Ping; Jian, Jin-Bao: A globally convergent QP-free algorithm for nonlinear semidefinite programming (2017)
  17. Wachsmuth, Gerd: Conforming approximation of convex functions with the finite element method (2017)
  18. Curtis, Frank E.; Gould, Nicholas I. M.; Jiang, Hao; Robinson, Daniel P.: Adaptive augmented Lagrangian methods: algorithms and practical numerical experience (2016)
  19. Polyak, Roman A.: The Legendre transformation in modern optimization (2016)
  20. Razavi, Hamidreza; Merat, Kaveh; Salarieh, Hassan; Alasty, Aria; Meghdari, Ali: Observer based minimum variance control of uncertain piecewise affine systems subject to additive noise (2016)

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