CONOPT is a generalized reduced-gradient (GRG) algorithm for solving large-scale nonlinear programs involving sparse nonlinear constraints. The paper will discuss strategic and tactical decisions in the development, upgrade, and maintenance of CONOPT over the last 8 years. A verbal and intuitive comparison of the GRG algorithm with the popular methods based on sequential linearized subproblems forms the basis for discussions of the implementation of critical components in a GRG code: basis factorizations, search directions, line-searches, and Newton iterations. The paper contains performance statistics for a range of models from different branches of engineering and economics of up to 4000 equations with comparative figures for MINOS version 5.3. Based on these statistics the paper concludes that GRG codes can be very competitive with other codes for large-scale nonlinear programming from both an efficiency and a reliability point of view. This is especially true for models with fairly nonlinear constraints, particularly when it is difficult to attain feasibility

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  1. Boukouvala, Fani; Faruque Hasan, M.M.; Floudas, Christodoulos A.: Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption (2017)
  2. Wang, Ximing; Pardalos, Panos M.: A modified active set algorithm for transportation discrete network design bi-level problem (2017)
  3. Wan, Wei; Biegler, Lorenz T.: Structured regularization for barrier NLP solvers (2017)
  4. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  5. Borraz-Sánchez, Conrado; Bent, Russell; Backhaus, Scott; Hijazi, Hassan; Van Hentenryck, Pascal: Convex relaxations for gas expansion planning (2016)
  6. Cai, Yongyang; Sanstad, Alan H.: Model uncertainty and energy technology policy: the example of induced technical change (2016)
  7. Castro, Pedro M.: Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems (2016)
  8. Pekár, Juraj; Čičková, Zuzana; Brezina, Ivan: Portfolio performance measurement using differential evolution (2016)
  9. Rose, Daniel; Schmidt, Martin; Steinbach, Marc C.; Willert, Bernhard M.: Computational optimization of gas compressor stations: MINLP models versus continuous reformulations (2016)
  10. Zhang, Yan; Sahinidis, Nikolaos V.: Global optimization of mathematical programs with complementarity constraints and application to clean energy deployment (2016)
  11. Cai, Yongyang; Judd, Kenneth L.: Dynamic programming with Hermite approximation (2015)
  12. Deo, Sarang; Rajaram, Kumar; Rath, Sandeep; Karmarkar, Uday S.; Goetz, Matthew B.: Planning for HIV screening, testing, and care at the veterans health administration (2015)
  13. Duarte, Belmiro P.M.; Wong, Weng Kee; Atkinson, Anthony C.: A semi-infinite programming based algorithm for determining T-optimum designs for model discrimination (2015)
  14. 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)
  15. Koch, Thorsten (ed.); Hiller, Benjamin (ed.); Pfetsch, Marc (ed.); Schewe, Lars (ed.): Evaluating gas network capacities (2015)
  16. Duarte, Belmiro P.M.; Wong, Weng Kee: A semi-infinite programming based algorithm for finding minimax optimal designs for nonlinear models (2014)
  17. Misener, Ruth; Floudas, Christodoulos A.: A framework for globally optimizing mixed-integer signomial programs (2014)
  18. Kolodziej, Scott; Castro, Pedro M.; Grossmann, Ignacio E.: Global optimization of bilinear programs with a multiparametric disaggregation technique (2013)
  19. Mínguez, Roberto; Conejo, Antonio J.; Castillo, Enrique: Optimal engineering design via Benders’ decomposition (2013)
  20. Bonami, Pierre; Kilinç, Mustafa; Linderoth, Jeff: Algorithms and software for convex mixed integer nonlinear programs (2012)

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