A Simplified Treatment of Ramana's Exact Dual for Semidefinite Programming

05/26/2022

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by   Bruno F. Lourenço, et al.

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In semidefinite programming the dual may fail to attain its optimal value and there could be a duality gap, i.e., the primal and dual optimal values may differ. In a striking paper, Ramana proposed a polynomial size extended dual that does not have these deficiencies and yields a number of fundamental results in complexity theory. In this work we walk the reader through a concise and self-contained derivation of Ramana's dual, relying mostly on elementary linear algebra.