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. Curtis, Frank E.; Gould, Nicholas I.M.; Robinson, Daniel P.; Toint, Philippe L.: An interior-point trust-funnel algorithm for nonlinear optimization (2017)
  2. Asadi, Alireza; Roos, Cornelis: Infeasible interior-point methods for linear optimization based on large neighborhood (2016)
  3. Curtis, Frank E.; Han, Zheng: Globally convergent primal-dual active-set methods with inexact subproblem solves (2016)
  4. Vanderbei, Robert; Lin, Kevin; Liu, Han; Wang, Lie: Revisiting compressed sensing: exploiting the efficiency of simplex and sparsification methods (2016)
  5. Dumont, Yves; Paoli, Laetitia: Dynamic contact of a beam against rigid obstacles: convergence of a velocity-based approximation and numerical results (2015)
  6. Janka, Dennis: Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential-algebraic equations (2015)
  7. Matějka, Filip: Rigid pricing and rationally inattentive consumer (2015)
  8. Sachsenberg, Björn; Schittkowski, Klaus: A combined SQP-IPM algorithm for solving large-scale nonlinear optimization problems (2015)
  9. Schmidt, Martin: An interior-point method for nonlinear optimization problems with locatable and separable nonsmoothness (2015)
  10. Benson, Hande Y.; Shanno, David F.: Interior-point methods for nonconvex nonlinear programming: cubic regularization (2014)
  11. Fernandes, Luís M.; Júdice, Joaquim J.; Sherali, Hanif D.; Forjaz, Maria A.: On an enumerative algorithm for solving eigenvalue complementarity problems (2014)
  12. Zhu, Zhichuan; Yu, Bo; Yang, Li: Globally convergent homotopy method for designing piecewise linear deterministic contractual function (2014)
  13. Bonami, Pierre; Kilinç, Mustafa; Linderoth, Jeff: Algorithms and software for convex mixed integer nonlinear programs (2012)
  14. Gondzio, Jacek: Interior point methods 25 years later (2012)
  15. Lantoine, Gregory; Russell, Ryan P.: A hybrid differential dynamic programming algorithm for constrained optimal control problems. I: Theory (2012)
  16. Le Thi, Hoai An; Moeini, Mahdi; Pham Dinh, Tao; Judice, Joaquim: A DC programming approach for solving the symmetric eigenvalue complementarity problem (2012)
  17. Li, Xianhong; Yu, Haibin; Yuan, Mingzhe: Modeling and optimization of cement raw materials blending process (2012)
  18. Mittelmann, Hans D.: The state-of-the-art in conic optimization software (2012)
  19. Simon, Jaan-Willem; Weichert, Dieter: Shakedown analysis with multidimensional loading spaces (2012)
  20. Vanderbei, Robert J.: Fast Fourier optimization (2012)

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