RAPOSa

The NEOS Server offers RAPOSa for the solution of global optimization and mixed-integer problems. Problems can be submitted to RAPOSa in AMPL format on the NEOS server.

RAPOSa (Reformulation Algorithm for Polynomial Optimization - Santiago) is a global optimization solver, specifically designed for mixed-integer polynomial programming problems with box-constrained variables. Written entirely in C++, it is based on the Reformulation-Linearization Technique developed by Hanif D. Sherali and Cihan H. Tuncbilek [5] and subsequently improved by Hanif D. Sherali, Evrim Dalkiran and collaborators [2] [3] [4]. To cite RAPOSa, please refer to this recently accepted paper in the Journal of Global Optimization: https://doi.org/10.1007/s10898-022-01229-w

The main features of RAPOSa are:

• Implementation of the basic RLT algorithm
• Efficient generation of bound factors via J-Sets
• Warm generation of J-Sets at each node
• Products of constraint factors and bound factors
• Bound tightening techniques
• SDP cuts
• Different branching criteria

RAPOSa is maintained by the development team of

• Ignacio Gómez Casares (Univ. de Santiago de Compostela)
• Julio González Díaz (Univ. de Santiago de Compostela)
• Brais González Rodríguez (Univ. de Santiago de Compostela)
• Beatriz Pateiro López (Univ. de Santiago de Compostela)

• [1]: González-Rodríguez, B., Ossorio-Castillo J., González-Díaz J., González-Rueda A. M., Rodríguez-Penas D. and Rodríguez-Martínez D., 2022. Computational advances in polynomial optimization: RAPOSa, a freely available global solver. Journal of Global Optimization, In press.
• [2]: Dalkiran, E. and Sherali, H.D., 2013. Theoretical filtering of RLT bound-factor constraints for solving polynomial programming problems to global optimality. Journal of Global Optimization, 57(4), pp. 1147-1172.
• [3]: Sherali, H. D., Dalkiran, E. and Desai, J., 2012. Enhancing RLT-based relaxations for polynomial programming problems via a new class of v-semidefinite cuts. Computational Optimization and Applications, 52(2), pp. 483-506.
• [4]: Sherali, H. D., Dalkiran, E. and Liberti, L., 2012. Reduced RLT representations for nonconvex polynomial programming problems. Journal of Global Optimization, 52(3), pp. 447-469.
• [5]: Sherali, H. D. and Tuncbilek, C. H., 1992. A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique. Journal of Global Optimization, 2(1), pp. 101-112.

Using the NEOS Server for RAPOSa/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 raposa_options 'OPTIONS';