GAMS/AlphaECP is a MINLP (Mixed-Integer Non-Linear Programming) solver based on the extended cutting plane (ECP) method. The solver can be applied to general MINLP problems and global optimal solutions can be ensured for pseudo-convex MINLP problems. The ECP method is an extension of Kelley’s cutting plane method which was originally given for convex NLP problems (Kelley, 1960). The method requires only the solution of a MIP sub problem in each iteration. The MIP sub problems may be solved to optimality, but can also be solved to feasibility or only to an integer relaxed solution in intermediate iterations. This makes the ECP algorithm efficient and easy to implement. Futher information about the underlying algorithm can be found in Westerlund T. and Pörn R. (2002). Solving Pseudo-Convex Mixed Integer Optimization Problems by Cutting Plane Techniques. Optimization and Engineering, 3. 253-280.

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  1. Kronqvist, Jan; Bernal, David E.; Grossmann, Ignacio E.: Using regularization and second order information in outer approximation for convex MINLP (2020)
  2. Burlacu, Robert; Egger, Herbert; Groß, Martin; Martin, Alexander; Pfetsch, Marc E.; Schewe, Lars; Sirvent, Mathias; Skutella, Martin: Maximizing the storage capacity of gas networks: a global MINLP approach (2019)
  3. Furini, Fabio; Traversi, Emiliano; Belotti, Pietro; Frangioni, Antonio; Gleixner, Ambros; Gould, Nick; Liberti, Leo; Lodi, Andrea; Misener, Ruth; Mittelmann, Hans; Sahinidis, Nikolaos V.; Vigerske, Stefan; Wiegele, Angelika: QPLIB: a library of quadratic programming instances (2019)
  4. Li, Can; Grossmann, Ignacio E.: A finite (\epsilon)-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables (2019)
  5. Schmidt, Martin; Sirvent, Mathias; Wollner, Winnifried: A decomposition method for MINLPs with Lipschitz continuous nonlinearities (2019)
  6. Wang, Tong; Lima, Ricardo M.; Giraldi, Loïc; Knio, Omar M.: Trajectory planning for autonomous underwater vehicles in the presence of obstacles and a nonlinear flow field using mixed integer nonlinear programming (2019)
  7. Cozad, Alison; Sahinidis, Nikolaos V.: A global MINLP approach to symbolic regression (2018)
  8. Delfino, A.; de Oliveira, W.: Outer-approximation algorithms for nonsmooth convex MINLP problems (2018)
  9. Khajavirad, Aida; Sahinidis, Nikolaos V.: A hybrid LP/NLP paradigm for global optimization relaxations (2018)
  10. Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio: Reformulations for utilizing separability when solving convex MINLP problems (2018)
  11. Oliphant, Terry-Leigh; Ali, M. Montaz: A trajectory-based method for mixed integer nonlinear programming problems (2018)
  12. Westerlund, Tapio; Eronen, Ville-Pekka; Mäkelä, Marko M.: On solving generalized convex MINLP problems using supporting hyperplane techniques (2018)
  13. Canca, David; De-Los-Santos, Alicia; Laporte, Gilbert; Mesa, Juan A.: An adaptive neighborhood search metaheuristic for the integrated railway rapid transit network design and line planning problem (2017)
  14. Eronen, Ville-Pekka; Kronqvist, Jan; Westerlund, Tapio; Mäkelä, Marko M.; Karmitsa, Napsu: Method for solving generalized convex nonsmooth mixed-integer nonlinear programming problems (2017)
  15. Canca, David; Barrena, Eva; Laporte, Gilbert; Ortega, Francisco A.: A short-turning policy for the management of demand disruptions in rapid transit systems (2016)
  16. de Oliveira, Welington: Regularized optimization methods for convex MINLP problems (2016)
  17. Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio: The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming (2016)
  18. van Ackooij, W.; Frangioni, A.; de Oliveira, W.: Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support (2016)
  19. Hiller, Benjamin; Humpola, Jesco; Lehmann, Thomas; Lenz, Ralf; Morsi, Antonio; Pfetsch, Marc E.; Schewe, Lars; Schmidt, Martin; Schwarz, Robert; Schweiger, Jonas; Stangl, Claudia; Willert, Bernhard M.: Computational results for validation of nominations (2015)
  20. Wei, Zhou; Ali, M. Montaz: Convex mixed integer nonlinear programming problems and an outer approximation algorithm (2015)

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