4 papers
Computing singular solutions of polynomial systems: towards superlinear convergence without deflation
Mikhail Karapetyants, Vladimir Kolmogorov, Jeferson Zapata
In Numerical Algebraic Geometry (NAG) isolated solutions of polynomial systems are usually computed by tracking a solution curve defined by a homotopy equation. The tracking proble…
Duality theory in linear optimization and its extensions -- formally verified
Martin Dvorak, Vladimir Kolmogorov
Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state…
Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified
Martin Dvorak, Tristan Figueroa-Reid, Rida Hamadani +8
Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory fa…
Certifying solutions of degenerate semidefinite programs
Vladimir Kolmogorov, Simone Naldi, Jeferson Zapata
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances a…