Efficiency of reliability-based design optimization (RBDO) methods is a critical criterion as to whether they are viable for real-world problems. Early RBDO methods are thus based primarily on the first-order reliability method (FORM) due to its efficiency. Recently, several first-order RBDO methods have been proposed, and their efficiency is significantly improved through problem reformulation and/or the use of inverse FORM. Our goal is to present these RBDO methods from a mathematical optimization perspective by formalizing FORM, inverse FORM, and associated RBDO reformulations. Through the formalization, their relationships are revealed. Using reported numerical studies, we discuss their numerical efficiency, convergence, and accuracy.

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