Ncpol2sdpa solves global polynomial optimization problems of either commutative variables or noncommutative operators through a semidefinite programming (SDP) relaxation. The optimization problem can be unconstrained or constrained by equalities and inequalities, and also by constraints on the moments. The objective is to be able to solve large scale optimization problems. Example applications include:

The implementation has an intuitive syntax for entering problems and it scales for a larger number of noncommutative variables using a sparse representation of the SDP problem. Further details are found in the following paper:

  • Peter Wittek. Algorithm 950: Ncpol2sdpa—Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables. ACM Transactions on Mathematical Software, 41(3), 21, 2015. DOI: 10.1145/2699464. arXiv:1308.6029.


This work is supported by the European Commission Seventh Framework Programme under Grant Agreement Number FP7-601138 PERICLES, by the Red Espanola de Supercomputacion grants number FI-2013-1-0008 and FI-2013-3-0004, and by the Swedish National Infrastructure for Computing projects SNIC 2014/2-7 and SNIC 2015/1-162.