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. Liu, Yanchao: A note on solving DiDi’s driver-order matching problem (2021)
  2. Chen, Rui; Qian, Xinwu; Miao, Lixin; Ukkusuri, Satish V.: Optimal charging facility location and capacity for electric vehicles considering route choice and charging time equilibrium (2020)
  3. Duarte, Belmiro P. M.; Granjo, José F. O.; Wong, Weng Kee: Optimal exact designs of experiments via mixed integer nonlinear programming (2020)
  4. Kim, Sun Hye; Boukouvala, Fani: Machine learning-based surrogate modeling for data-driven optimization: a comparison of subset selection for regression techniques (2020)
  5. Marandi, Ahmadreza; de Klerk, Etienne; Dahl, Joachim: Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy (2020)
  6. Awasthi, Utsav; Marmier, Remy; Grossmann, Ignacio E.: Multiperiod optimization model for oilfield production planning: bicriterion optimization and two-stage stochastic programming model (2019)
  7. 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)
  8. Kimizuka, Masaki; Kim, Sunyoung; Yamashita, Makoto: Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods (2019)
  9. Ogbe, Emmanuel; Li, Xiang: A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs (2019)
  10. Paternain, Santiago; Mokhtari, Aryan; Ribeiro, Alejandro: A Newton-based method for nonconvex optimization with fast evasion of saddle points (2019)
  11. Schewe, Lars; Schmidt, Martin: Computing feasible points for binary MINLPs with MPECs (2019)
  12. Schweidtmann, Artur M.; Mitsos, Alexander: Deterministic global optimization with artificial neural networks embedded (2019)
  13. Teter, Michael D.; Royset, Johannes O.; Newman, Alexandra M.: Modeling uncertainty of expert elicitation for use in risk-based optimization (2019)
  14. 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)
  15. Amaya Moreno, Liana; Fügenschuh, Armin; Kaier, Anton; Schlobach, Swen: A nonlinear model for vertical free-flight trajectory planning (2018)
  16. Consiglio, Andrea; Tumminello, Michele; Zenios, Stavros A.: Pricing sovereign contingent convertible debt (2018)
  17. Duarte, Belmiro P. M.; Sagnol, Guillaume; Wong, Weng Kee: An algorithm based on semidefinite programming for finding minimax optimal designs (2018)
  18. Duarte, Belmiro P. M.; Wong, Weng Kee; Dette, Holger: Adaptive grid semidefinite programming for finding optimal designs (2018)
  19. Gao, Wei; Wu, Di; Gao, Kang; Chen, Xiaojun; Tin-Loi, Francis: Structural reliability analysis with imprecise random and interval fields (2018)
  20. Khajavirad, Aida; Sahinidis, Nikolaos V.: A hybrid LP/NLP paradigm for global optimization relaxations (2018)

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