computer algebra – Optimization Online

SPECTRA – a Maple library for solving linear matrix inequalities in exact arithmetic

Published: 2016/11/05

Semi-definite Programming computer algebra, linear matrix inequalities, low-rank matrices, polynomial sums of squares, semidefinite programming

This document briefly describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities in exact arithmetic and it is targeted to small-size, possibly degenerate problems for which symbolic infeasibility or feasibility certificates are required. ArticleDownload View PDF

Solving rank-constrained semidefinite programs in exact arithmetic

Published: 2016/02/01, Updated: 2016/09/19

Simone Naldi

Semi-definite Programming computer algebra, determinantal varieties, exact algorithms, linear matrix inequalities, polynomial optimization, rank constraints, semidefinite programming, spectrahedra, sums-of-squares

We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active, this is a non-convex optimization problem, otherwise it is a semidefinite program. Both find numerous applications especially in … Read more