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Showing 1 to 11 of 11 for “"Quasi-Newton methods"”.
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Quasi-Newton Methods for Nonlinear Programming
… a new 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
… convergence 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 …
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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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Solving The Prandtl Boundary Layer Equation in Fluid Dynamics Via Non-Linear Numerical Optimization
… of 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
… and 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 …
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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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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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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 …