A Discrete Lagrangian Algorithm for Optimal Routing Problems - Kosmas, Odysseas; Vlachos, Dimitros S; Simos, Theodoros E. (AIP Conference Proceedings, 2007)
The ideas of discrete <named-content content-type="sem:AIPTh1.2" rid="kwd1.1" style="color: rgb(0, 0, 0); font-family: Lora, serif; font-size: 20px;" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://www.niso.org/standards/z39-96/ns/oasis-exchange/table" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton’s principle of stationary action <named-content content-type="sem:AIPTh1.2" rid="kwd1.1" style="color: rgb(0, 0, 0); font-family: Lora, serif; font-size: 20px;" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://www.niso.org/standards/z39-96/ns/oasis-exchange/table" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">Lagrangian and specifically on the direct discretization of the Lagrange‐Hamilton principle for a conservative system. Since, in contrast to the <named-content content-type="sem:AIPTh1.2" rid="kwd1.2" style="color: rgb(0, 0, 0); font-family: Lora, serif; font-size: 20px;" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://www.niso.org/standards/z39-96/ns/oasis-exchange/table" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">differential equations, the discrete Euler‐Lagrange <named-content content-type="sem:AIPTh1.2" rid="kwd1.1 kwd1.2" style="color: rgb(0, 0, 0); font-family: Lora, serif; font-size: 20px;" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://www.niso.org/standards/z39-96/ns/oasis-exchange/table" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.
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