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Showing 1 to 6 of 6 for “"Lagrangian functions"”.
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Lagrangian Mechanics Modeling of Free Surface-Affected Marine Craft
… operator training. In this dissertation, Lagrangian mechanics is used to derive nonlinear, parametric motion models for marine craft operating in the presence of a free surface. In Lagrangian mechanics, one constructs the equations of motion for a dynamic system using a system Lagrangian, …
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Mathematical algorithms for optimisation of large scale systems
… information which is mainly based on the normal Lagrangian function. Two existing algorithms are examined: The double iterative price correction mechanism and the augmented interaction balance method. Both methods use a double iterative coordination strategy and global feedback measurements from …
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A virtual element method for hyperelasticity
… respectively. Furthermore, the local basis functions are not known explicitly on elements and take the simple form of piecewise-linear Lagrangian functions on element boundaries. All integrations are performed on element edges. The VEM formulation typically involves a consistency term, …
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First Order Methods for Large-Scale Sparse Optimization
… and then to solve a single penalty or Lagrangian problem. However, these methods generally do not guarantee convergence to feasibility. The focus of this thesis is on developing new fast first-order iterative algorithms for computing sparse and low-rank solutions to large-scale …
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Algorithms for Sparse and Low-Rank Optimization: Convergence, Complexity and Applications
… are based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions. Our basic methods require at most O(1/ε) iterations to obtain an ε-optimal solution, while our accelerated (i.e., fast) versions require at most O(1/√ε) iterations, with little …
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Optimization Algorithms for Structured Machine Learning and Image Processing Problems
… a unified framework based on the augmented Lagrangian method, under which problems with both types of regularization and their variants can be efficiently solved. As one of the core building-blocks of this framework, we develop new algorithms using a partial-linearization/splitting technique …