Free Shape Optimal Design of Structures

Bletzinger, Kai‐Uwe

doi:10.1007/978-3-642-23435-4_4

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2023

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“…Remark 8. This section focuses on the vanilla implementation of GDAM and demonstrates its robustness in solving node-based shape optimization problems, as robustness is considered a key to practical success for real-world shape design applications [20]. Accelerated GDAM can be applied to further reduce the number of iterations.…”

Section: Real-world Examplementioning

confidence: 99%

A gradient descent akin method for constrained optimization: algorithms and applications

Chen¹,

Bletzinger²,

Gauger³

et al. 2023

Preprint

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We present a first-order method for solving constrained optimization problems. The method is derived from our previous work [28], a modified search direction method inspired by singular value decomposition. In this work, we simplify its computational framework to a "gradient descent akin" method (GDAM), i.e., the search direction is computed using a linear combination of the negative and normalized objective and constraint gradient. We give fundamental theoretical guarantees on the global convergence of the method. This work focuses on the algorithms and applications of GDAM. We present computational algorithms that adapt common strategies for the gradient descent method. We demonstrate the potential of the method using two engineering applications, shape optimization and sensor network localization. When practically implemented, GDAM is robust and very competitive in solving the considered large and challenging optimization problems.

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Section: Real-world Examplementioning

confidence: 99%