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math.OC2024
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…
math.OC2024
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…