LOQO: An interior point code for quadratic programming. This paper describes a software package, called LOQO, which implements a primal-dual interior-point method for general nonlinear programming. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programming with only brief mention of the extensions to convex and general nonlinear programming, since a detailed paper describing these extensions was published recently elsewhere. In particular, we emphasize the importance of establishing and maintaining symmetric quasidefiniteness of the reduced KKT system. We show that the industry standard MPS format can be nicely formulated in such a way to provide quasidefiniteness. Computational results are included for a variety of linear and quadratic programming problems.

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  1. Adjé, Assalé: Quadratic maximization of reachable values of affine systems with diagonalizable matrix (2021)
  2. Galvan, Giulio; Lapucci, Matteo; Lin, Chih-Jen; Sciandrone, Marco: A two-level decomposition framework exploiting first and second order information for SVM training problems (2021)
  3. Liu, Defeng; Lodi, Andrea; Tanneau, Mathieu: Learning chordal extensions (2021)
  4. Zuo, Yijun: Computation of projection regression depth and its induced median (2021)
  5. Casanellas, Glòria; Castro, Jordi: Using interior point solvers for optimizing progressive lens models with spherical coordinates (2020)
  6. Vanderbei, Robert J.: Linear programming. Foundations and extensions (2020)
  7. Ballard, Grey; Ikenmeyer, Christian; Landsberg, J. M.; Ryder, Nick: The geometry of rank decompositions of matrix multiplication. II: (3 \times3) matrices (2019)
  8. Cimini, Gionata; Bemporad, Alberto: Complexity and convergence certification of a block principal pivoting method for box-constrained quadratic programs (2019)
  9. Jin, Shaobo; Ankargren, Sebastian: Frequentist model averaging in structural equation modelling (2019)
  10. Paternain, Santiago; Mokhtari, Aryan; Ribeiro, Alejandro: A Newton-based method for nonconvex optimization with fast evasion of saddle points (2019)
  11. Kuhlmann, Renke; Büskens, Christof: A primal-dual augmented Lagrangian penalty-interior-point filter line search algorithm (2018)
  12. Le Thi, Hoai An; Huynh, Van Ngai; Pham Dinh, Tao: Convergence analysis of difference-of-convex algorithm with subanalytic data (2018)
  13. Le Thi, Hoai An; Pham Dinh, Tao: DC programming and DCA: thirty years of developments (2018)
  14. Qiu, Songqiang; Chen, Zhongwen: An interior point method for nonlinear optimization with a quasi-tangential subproblem (2018)
  15. Armand, Paul; Omheni, Riadh: A mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization (2017)
  16. Breedveld, Sebastiaan; van den Berg, Bas; Heijmen, Ben: An interior-point implementation developed and tuned for radiation therapy treatment planning (2017)
  17. Curtis, Frank E.; Gould, Nicholas I. M.; Robinson, Daniel P.; Toint, Philippe L.: An interior-point trust-funnel algorithm for nonlinear optimization (2017)
  18. Gould, Nicholas I. M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
  19. Le Thi, Hoai An; Pham Dinh, Tao: Difference of convex functions algorithms (DCA) for image restoration via a Markov random field model (2017)
  20. Wan, Wei; Biegler, Lorenz T.: Structured regularization for barrier NLP solvers (2017)

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