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. Paternain, Santiago; Mokhtari, Aryan; Ribeiro, Alejandro: A Newton-based method for nonconvex optimization with fast evasion of saddle points (2019)
  2. Schweidtmann, Artur M.; Mitsos, Alexander: Deterministic global optimization with artificial neural networks embedded (2019)
  3. 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)
  4. Amaya Moreno, Liana; Fügenschuh, Armin; Kaier, Anton; Schlobach, Swen: A nonlinear model for vertical free-flight trajectory planning (2018)
  5. Consiglio, Andrea; Tumminello, Michele; Zenios, Stavros A.: Pricing sovereign contingent convertible debt (2018)
  6. Duarte, Belmiro P. M.; Sagnol, Guillaume; Wong, Weng Kee: An algorithm based on semidefinite programming for finding minimax optimal designs (2018)
  7. Duarte, Belmiro P. M.; Wong, Weng Kee; Dette, Holger: Adaptive grid semidefinite programming for finding optimal designs (2018)
  8. Khajavirad, Aida; Sahinidis, Nikolaos V.: A hybrid LP/NLP paradigm for global optimization relaxations (2018)
  9. Kılınç, Mustafa R.; Sahinidis, Nikolaos V.: Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with BARON (2018)
  10. Pineda, S.; Bylling, H.; Morales, J. M.: Efficiently solving linear bilevel programming problems using off-the-shelf optimization software (2018)
  11. Post, Thierry; Karabatı, Selçuk; Arvanitis, Stelios: Portfolio optimization based on stochastic dominance and empirical likelihood (2018)
  12. Andrei, Neculai: Continuous nonlinear optimization for engineering applications in GAMS technology (2017)
  13. Bongartz, Dominik; Mitsos, Alexander: Deterministic global optimization of process flowsheets in a reduced space using McCormick relaxations (2017)
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  15. Geißler, Björn; Morsi, Antonio; Schewe, Lars; Schmidt, Martin: Penalty alternating direction methods for mixed-integer optimization: a new view on feasibility pumps (2017)
  16. Klimeš, Lubomír; Popela, Pavel; Mauder, Tomáš; Štětina, Josef; Charvát, Pavel: Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface. (2017)
  17. Lasdon, Leon; Shirzadi, Shawn; Ziegel, Eric: Implementing CRM models for improved oil recovery in large oil fields (2017)
  18. Leimbach, Marian; Schultes, Anselm; Baumstark, Lavinia; Giannousakis, Anastasis; Luderer, Gunnar: Solution algorithms for regional interactions in large-scale integrated assessment models of climate change (2017)
  19. Sioshansi, Ramteen; Conejo, Antonio J.: Optimization in engineering. Models and algorithms (2017)
  20. Wang, Ximing; Pardalos, Panos M.: A modified active set algorithm for transportation discrete network design bi-level problem (2017)

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