Optimal design with probabilistic objective and constraints

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A survey on approaches for reliability-based optimization (2010, background): “In subsequent contributions, the semi-infinite approximation of the RBO problem was extended to cover the case of minimization of an expected cost function ( Royset et al. 2001b, 2006 ).”
Single-loop system reliability-based topology optimization considering statistical dependence between limit-states (2011, methodology): “For example, Royset et al. (2006) employed the first-order approximation for failure probability and then used higher-order reliability approximations or Monte Carlo simulations to adjust parameters to improve the accuracy of system reliability-based design optimization.”
Extensions of Stochastic Optimization Results to Problems with System Failure Probability Functions (2007, methodology): “In comparison, the design obtained in [12] has a somewhat larger cost of 13.”
A tractable approximation of non-convex chance constrained optimization with non-Gaussian uncertainties (2015, background): “…finance and economics (Charnes and Cooper 1959; Rockafellar and Uryasev 2000; Wozabal 2012; Wozabal, Hochreiter, and Pflug 2010); reliability based design optimization (Royset, Kiureghian, and Polak 2006, and references therein); robotic systems (Blackmore et al. 2010), to mention only a very few.”