The author presents a modification of a variational principle of \textit{A. D. Ioffe} and \textit{A. J. Zaslavski} [SIAM J. Control Optimization 38, No.~2, 566-581 (2000; Zbl 0997.49023)] in which the conclusion of the result is strengthened to read that the complement of the well-posed optimization problems in a given class is \(\sigma\)-porous in the class, instead of being only a first Baire category set in the class. The notion of a \(\sigma\)-porous set is a strict refinement of the notion of first Baire category set in any metric space without isolated points as well as a strict refinement of the Lebesgue measure zero set in finite dimensions. The modification is then applied to several concrete classes of optimization problems.