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Showing 1 to 20 of 20 for “"Newton methods"”.
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Quasi-Newton Methods for Nonlinear Programming
… class of symmetric updates for use in a quasi-Newton method for nonlinear programming. We show how these updates model the underlying nonlinear equation better than the standard symmetric updates and also how they require less overall work for large problems.
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On the Use of Quasi-Newton Methods for the Minimization of Convex Quadratic Splines
<p>In reformulating a strictly convex quadratic program with simple bound constraints as the unconstrained minimization of a strictly convex quadratic spline, established algorithms can be implemented with relaxed differentiability conditions. In this work, the positive definite secant update …
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Quasi-Newton and Multigrid Methods for Semiconductor Device Simulation
… analysis of Gummel's method and quasi-Newton methods is extended to a nonuniform mesh and the Bernoulli function discretization. It is proved that Gummel's method and the quasi-Newton methods for the scaled carrier densities and carrier densities converge locally for sufficiently smooth …
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Matrix Factorizations, Triadic Matrices, and Modified Cholesky Factorizations for Optimization
… of symmetric matrices and their application to Newton-type optimization. A matrix is called triadic if it has at most two nonzero off-diagonal elements in each column. Tridiagonal matrices are a special case of these. We prove that the triadic structure is preserved in the Cholesky-related …
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Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation
… subspace iteration. We also examine Newton methods for general large sparse eigenvalue problems satisfying the overdamping condition and show how to use sparse iterative solvers more effectively in them.
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An Examination of the Strengths and Weaknesses of Newton's Method for Nonlinear Optimization
… linear and nonlinear optimization. While other methods are mentioned, the focus is on analytical methods used to solve nonlinear optimization problems. We briefly look at some of the most effective constrained methods for nonlinear optimization and then show how unconstrained methods often play …
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Spectral methods for circuit analysis
Harmonic balance (HB) methods are frequency-domain algorithms used for high accuracy computation of the periodic steady-state of circuits. Matrix-implicit Krylov-subspace techniques have made it possible for these methods to simulate large circuits more efficiently. However, the harmonic balance …
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Advances in Optimisation of Model Parameters and Hyperparameters for Neural Networks
… which carry considerable computational cost. Methods based on hypergradients use only one training pass, but these either cannot be applied to arbitrary optimiser hyperparameters (such as learning rates and momenta) or suffer considerable additional training time. In an extension to these …
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Continuous Low-Thrust Trajectory Optimization: Techniques and Applications
… scheme based on numerical and analytical methods. Whereas other conventional optimization packages rely on numerical solution approaches, we employ analytical and semi-analytical techniques such as symmetry and homotopy methods to assist in the solution-finding process. The first objective …
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Randomization for Efficient Nonlinear Parametric Inversion
… prohibitive. In this thesis, we introduce two methods to drastically reduce this cost. To efficiently implement Newton methods, we extend the use of simultaneous random sources to reduce the number of linear system solves to include simultaneous random detectors. Moreover, we combine …
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Solving The Prandtl Boundary Layer Equation in Fluid Dynamics Via Non-Linear Numerical Optimization
… O(h4) or O(h6).A powerful variation of the Quasi-Newton methods known as the BFGS Quasi-Newton iteration is applied with a quadratic convergence rate [41][43] while the conventional FVM converges linearly using the SIMPLE iteration approach. In this work, an Objective Function (or Penalty …
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New PDE models for imaging problems and applications
Variational methods and Partial Differential Equations (PDEs) have been extensively employed for the mathematical formulation of a myriad of problems describing physical phenomena such as heat propagation, thermodynamic transformations and many more. In imaging, PDEs following variational …
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Limited Memory Space Dilation and Reduction Algorithms
… limited memory updates for differentiable quasi-Newton methods. This well known r-algorithm, which employs a space dilation strategy in the direction of the difference between two successive subgradients, is recognized as being one of the most effective procedures for solving nondifferentiable …
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Analysis of Acceleration Techniques and Fast Nonlinear Solvers
… connections between residual-based acceleration methods and Krylov subspace techniques. The first main contribution is a unified algebraic framework establishing the equivalence between the Anderson Acceleration method and the CROP (Conjugate Residual with Optimal Trial Vector) algorithm. By …
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Bridging Machine Learning for Smart Grid Applications
… (WLS) algorithm and solved using iterative methods such as Gauss-Newton methods. However, iterative methods have become more sensitive to system operating conditions than ever before due to the deployment of intermittent renewable energy sources, zero-emission technologies (e.g., electric …
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Spectral Optimization Problems Controlling Wave Phenomena
… problem is solved numerically using a quasi-Newton method. The method is applied to maximizing two particular nonsmooth functions of the eigenvalues: (a) the ratio of the n-th to first eigenvalues and (b) the ratio of the n-th eigenvalue gap to first eigenvalue. Both are generalizations of …
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Viscoelastic Fluid Modeling for Geophysical Applications in an Eulerian Framework
… solved using semi-implicit time integration and Newton's method. Numerical verification and validation, including the method of manufactured solutions, reveal challenges in achieving mesh-convergent solutions under uniform refinement. Finally, we compare the proposed models against classical …
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Efficient algorithms for flow models coupled with geomechanics for porous media applications
… flow and mechanics schemes. The global inexact Newton method, combined with the line search backtracking algorithm along with heuristic forcing functions, can be efficiently employed to reduce the number of flow linear iterations, and hence, the overall CPU run time. We first validate these …