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. Armand, Paul; Omheni, Riadh: A mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization (2017)
  2. Curtis, Frank E.; Gould, Nicholas I.M.; Robinson, Daniel P.; Toint, Philippe L.: An interior-point trust-funnel algorithm for nonlinear optimization (2017)
  3. Gould, Nicholas I.M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
  4. Wan, Wei; Biegler, Lorenz T.: Structured regularization for barrier NLP solvers (2017)
  5. Yang, Yaguang: CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming (2017)
  6. Zhu, Zhichuan; Yu, Bo: Globally convergent homotopy algorithm for solving the KKT systems to the principal-agent bilevel programming (2017)
  7. Asadi, Alireza; Roos, Cornelis: Infeasible interior-point methods for linear optimization based on large neighborhood (2016)
  8. Curtis, Frank E.; Han, Zheng: Globally convergent primal-dual active-set methods with inexact subproblem solves (2016)
  9. Vanderbei, Robert; Lin, Kevin; Liu, Han; Wang, Lie: Revisiting compressed sensing: exploiting the efficiency of simplex and sparsification methods (2016)
  10. Dumont, Yves; Paoli, Laetitia: Dynamic contact of a beam against rigid obstacles: convergence of a velocity-based approximation and numerical results (2015)
  11. Janka, Dennis: Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential-algebraic equations (2015)
  12. Matějka, Filip: Rigid pricing and rationally inattentive consumer (2015)
  13. Sachsenberg, Björn; Schittkowski, Klaus: A combined SQP-IPM algorithm for solving large-scale nonlinear optimization problems (2015)
  14. Schmidt, Martin: An interior-point method for nonlinear optimization problems with locatable and separable nonsmoothness (2015)
  15. Armand, Paul; Benoist, Joël; Omheni, Riadh; Pateloup, Vincent: Study of a primal-dual algorithm for equality constrained minimization (2014)
  16. Benson, Hande Y.; Shanno, David F.: Interior-point methods for nonconvex nonlinear programming: cubic regularization (2014)
  17. Fernandes, Luís M.; Júdice, Joaquim J.; Sherali, Hanif D.; Forjaz, Maria A.: On an enumerative algorithm for solving eigenvalue complementarity problems (2014)
  18. Keller, Philipp W.; Levi, Retsef; Perakis, Georgia: Efficient formulations for pricing under attraction demand models (2014)
  19. Zhu, Zhichuan; Yu, Bo; Yang, Li: Globally convergent homotopy method for designing piecewise linear deterministic contractual function (2014)
  20. Bonami, Pierre; Kilinç, Mustafa; Linderoth, Jeff: Algorithms and software for convex mixed integer nonlinear programs (2012)

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