SPECTRA -- a Maple library for solving linear matrix inequalities in exact arithmetic
Mohab Safey El Din (PolSys), Didier Henrion (LAAS-MAC, CTU), Simone, Naldi (TU), Mohab Safey, El Din
TL;DR
SPECTRA is a Maple library designed for solving linear matrix inequalities exactly using symbolic computation, particularly suited for small, possibly degenerate problems requiring precise feasibility certificates.
Contribution
It introduces a freely available Maple library that enables exact symbolic solutions to linear matrix inequalities in semidefinite programming.
Findings
Enables exact symbolic solutions for small LMIs
Provides certificates of feasibility or infeasibility
Facilitates research requiring precise algebraic verification
Abstract
This document describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities with symbolic computation in exact arithmetic and it is targeted to small-size, possibly degenerate problems for which symbolic infeasibility or feasibility certificates are required.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Polynomial and algebraic computation · Matrix Theory and Algorithms