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• W3136378834 abstract "This chapter focuses on the formulation of the optimization problem in expectation. It considers the problem stated with the mean objective functions. The chapter shows how it is possible to reformulate a reliability-based optimization problem into a multiobjective stochastic optimization problem. Descent algorithms require the construction of a common descent direction for each objective of the optimization problem. The construction of such a direction, if it exists, is based on convex analysis results. The chapter illustrates the notion of subdifferential of a convex function. It introduces the principle of optimization and the notion of minimum of an ordered and preordered set. The chapter presents Pareto preorder which is one of the binary relations used in the framework of multiobjective optimization. It defines the notion of the common descent vector. Multiple gradient descent algorithm is a descent algorithm based on the existence and construction of a descent vector common to the set of iteration objectives." @default.
• W3136378834 created "2021-03-29" @default.
• W3136378834 creator A5012084451 @default.
• W3136378834 creator A5071856697 @default.
• W3136378834 date "2021-03-19" @default.
• W3136378834 modified "2023-10-03" @default.
• W3136378834 title "Stochastic Multiobjective Optimization: A Descent Algorithm" @default.
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• W3136378834 doi "https://doi.org/10.1002/9781119817635.ch8" @default.
• W3136378834 hasPublicationYear "2021" @default.
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