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In order to verify programs or hybrid systems, one often needs to prove thatcertain formulas are unsatisfiable. In this paper, we consider conjunctions ofpolynomial inequalities over the reals. Classical algorithms for deciding thesenot only have high complexity, but also provide no simple proof ofunsatisfiability. Recently, a reduction of this problem to semidefiniteprogramming and numerical resolution has been proposed. In this article, weshow how this reduction generally produces degenerate problems on whichnumerical methods stumble.

Fatal Degeneracy in the Semidefinite Programming Approach to the Decision of Polynomial Inequalities