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. Paternain, Santiago; Mokhtari, Aryan; Ribeiro, Alejandro: A Newton-based method for nonconvex optimization with fast evasion of saddle points (2019)
  2. Bacci, Giovanni; Bacci, Giorgio; Larsen, Kim G.; Mardare, Radu: On the metric-based approximate minimization of Markov chains (2018)
  3. Lourenço, Bruno F.; Fukuda, Ellen H.; Fukushima, Masao: Optimality conditions for nonlinear semidefinite programming via squared slack variables (2018)
  4. Shen, Xin; Mitchell, John E.: A penalty method for rank minimization problems in symmetric matrices (2018)
  5. Zhao, Qi; Chen, Zhongwen: An SQP-type method with superlinear convergence for nonlinear semidefinite programming (2018)
  6. Armand, Paul; Omheni, Riadh: A mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization (2017)
  7. Li, Jian-Ling; Yang, Zhen-Ping; Jian, Jin-Bao: A globally convergent QP-free algorithm for nonlinear semidefinite programming (2017)
  8. Wachsmuth, Gerd: Conforming approximation of convex functions with the finite element method (2017)
  9. Curtis, Frank E.; Gould, Nicholas I. M.; Jiang, Hao; Robinson, Daniel P.: Adaptive augmented Lagrangian methods: algorithms and practical numerical experience (2016)
  10. Polyak, Roman A.: The Legendre transformation in modern optimization (2016)
  11. 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)
  12. Saldivar, Belem; Mondié, Sabine; Ávila Vilchis, Juan Carlos: The control of drilling vibrations: a coupled PDE-ODE modeling approach (2016)
  13. Zhao, Qi; Chen, Zhongwen: On the superlinear local convergence of a penalty-free method for nonlinear semidefinite programming (2016)
  14. Curtis, Frank E.; Jiang, Hao; Robinson, Daniel P.: An adaptive augmented Lagrangian method for large-scale constrained optimization (2015)
  15. Gould, Nicholas I. M.; Loh, Yueling; Robinson, Daniel P.: A nonmonotone filter SQP method: local convergence and numerical results (2015)
  16. Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.: CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization (2015)
  17. Kato, Atsushi; Yabe, Hiroshi; Yamashita, Hiroshi: An interior point method with a primal-dual quadratic barrier penalty function for nonlinear semidefinite programming (2015)
  18. Michal Kocvara, Michael Stingl: PENNON: Software for linear and nonlinear matrix inequalities (2015) arXiv
  19. Mohy-ud-Din, Hassan; Robinson, Daniel P.: A solver for nonconvex bound-constrained quadratic optimization (2015)
  20. Robinson, Daniel P.: Primal-dual active-set methods for large-scale optimization (2015)

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