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.

References in zbMATH (referenced in 31 articles )

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  1. Canca, David; Barrena, Eva; Laporte, Gilbert; Ortega, Francisco A.: A short-turning policy for the management of demand disruptions in rapid transit systems (2016)
  2. de Oliveira, Welington: Regularized optimization methods for convex MINLP problems (2016)
  3. Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio: The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming (2016)
  4. van Ackooij, W.; Frangioni, A.; de Oliveira, W.: Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support (2016)
  5. 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)
  6. Wei, Zhou; Ali, M.Montaz: Generalized Benders decomposition for one class of MINLPs with vector conic constraint (2015)
  7. Wei, Zhou; Ali, M.Montaz: Convex mixed integer nonlinear programming problems and an outer approximation algorithm (2015)
  8. Patil, Bhagyesh V.; Nataraj, P.S.V.: An improved Bernstein global optimization algorithm for MINLP problems with application in process industry (2014)
  9. D’ambrosio, Claudia; Lodi, Andrea: Mixed integer nonlinear programming tools: an updated practical overview (2013)
  10. Li, Min; Vicente, Luís Nunes: Inexact solution of NLP subproblems in MINLP (2013)
  11. Van Dinter, Jennifer; Rebennack, Steffen; Kallrath, Josef; Denholm, Paul; Newman, Alexandra: The unit commitment model with concave emissions costs: a hybrid Benders’ decomposition with nonconvex master problems (2013)
  12. Bonami, Pierre; Kilinç, Mustafa; Linderoth, Jeff: Algorithms and software for convex mixed integer nonlinear programs (2012)
  13. Exler, Oliver; Lehmann, Thomas; Schittkowski, Klaus: A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization (2012)
  14. Grossmann, Ignacio E.; Ruiz, Juan P.: Generalized disjunctive programming: a framework for formulation and alternative algorithms for MINLP optimization (2012)
  15. Nikulin, Yury; Miettinen, Kaisa; Mäkelä, Marko M.: A new achievement scalarizing function based on parameterization in multiobjective optimization (2012)
  16. Ruiz, Juan P.; Grossmann, Ignacio E.: A hierarchy of relaxations for nonlinear convex generalized disjunctive programming (2012)
  17. D’Ambrosio, Claudia; Lodi, Andrea: Mixed integer nonlinear programming tools: a practical overview (2011)
  18. Zhu, Wenxing; Lin, Geng: A dynamic convexized method for nonconvex mixed integer nonlinear programming (2011)
  19. Nannicini, Giacomo: Point-to-point shortest paths on dynamic time-dependent road networks (2010)
  20. Jüdes, Marc; Vigerske, Stefan; Tsatsaronis, George: Optimization of the design and partial-load operation of power plants using mixed-integer nonlinear programming (2009)

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