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. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  2. Castro, Pedro M.: Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems (2016)
  3. Pekár, Juraj; Čičková, Zuzana; Brezina, Ivan: Portfolio performance measurement using differential evolution (2016)
  4. Rose, Daniel; Schmidt, Martin; Steinbach, Marc C.; Willert, Bernhard M.: Computational optimization of gas compressor stations: MINLP models versus continuous reformulations (2016)
  5. Zhang, Yan; Sahinidis, Nikolaos V.: Global optimization of mathematical programs with complementarity constraints and application to clean energy deployment (2016)
  6. Cai, Yongyang; Judd, Kenneth L.: Dynamic programming with Hermite approximation (2015)
  7. 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)
  8. 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)
  9. Duarte, Belmiro P.M.; Wong, Weng Kee: A semi-infinite programming based algorithm for finding minimax optimal designs for nonlinear models (2014)
  10. Misener, Ruth; Floudas, Christodoulos A.: A framework for globally optimizing mixed-integer signomial programs (2014)
  11. Kolodziej, Scott; Castro, Pedro M.; Grossmann, Ignacio E.: Global optimization of bilinear programs with a multiparametric disaggregation technique (2013)
  12. Mínguez, Roberto; Conejo, Antonio J.; Castillo, Enrique: Optimal engineering design via Benders’ decomposition (2013)
  13. Bonami, Pierre; Kilinç, Mustafa; Linderoth, Jeff: Algorithms and software for convex mixed integer nonlinear programs (2012)
  14. Morales, José Luis; Nocedal, Jorge; Wu, Yuchen: A sequential quadratic programming algorithm with an additional equality constrained phase (2012)
  15. Takano, Yuichi; Sotirov, Renata: A polynomial optimization approach to constant rebalanced portfolio selection (2012)
  16. Al-Najjar, Camelia; Malakooti, Behnam: Hybrid-LP: finding advanced starting points for simplex, and pivoting LP methods (2011)
  17. Bruni, M.E.; Beraldi, P.; Guerriero, F.; Pinto, E.: A heuristic approach for resource constrained project scheduling with uncertain activity durations (2011)
  18. Byrd, Richard H.; Waltz, Richard A.: An active-set algorithm for nonlinear programming using parametric linear programming (2011)
  19. Matousek, Radomil; Zampachova, Eva: Promising GAHC and HC12 algorithms in global optimization tasks (2011)
  20. Ruiz, Juan P.; Grossmann, Ignacio E.: Exploiting vector space properties to strengthen the relaxation of bilinear programs arising in the global optimization of process networks (2011)

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