LOQO

The NEOS Server offers LOQO for the solution of nonlinearly-constrained optimization problems. Problems can be submitted to LOQO on the NEOS server in AMPL format.

LOQO is based on an infeasible primal-dual interior-point method and solves both convex and nonconvex optimization problems. Subject to the requirement that the defining functions be smooth (at the points evaluated by the algorithm), LOQO can handle a range of problems: linear or nonlinear, convex or nonconvex, constrained or unconstrained. For convex problems, LOQO finds a globally optimal solution; otherwise, it iterates from the given starting point to find a locally optimal solution.

LOQO was developed by Robert J. Vanderbei and Hande Y. Benson. Additional information for LOQO is available in the LOQO User's Manual (Version 4.05).

References:

• Shanno, D. F. and Vanderbei, R. J. 2000. Interior-Point Methods for Nonconvex Nonlinear Programming: Orderings and Higher-Order Methods. Mathematical Programming 87(2): 303-316.
• Vanderbei, R. J. 1999. LOQO: An interior point code for quadratic programming. Optimization Methods and Software 12: 451-484.
• Vanderbei, R. J. and Shanno, D. F. 1999. An Interior-Point Algorithm for Nonconvex Nonlinear Programming. Computational Optimization and Applications 13: 231-252.

Using the NEOS Server for LOQO/AMPL

The user must submit a model in AMPL format. Examples are provided in the examples section of the AMPL website.

The problem must be specified in a model file. A data file and commands files may also be provided. If the commands file is specified, it must contain the AMPL solve command; however, it must not contain the model or data commands. The model and data files are renamed internally by NEOS.

The commands file may include option settings for the solver. To specify solver options, add

  option loqo_options 'OPTIONS';