Concept

Newton's method in optimization

Related lectures (28)

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Newton's Method for Dynamical Systems

Explores Newton's method for dynamical systems, GMRES, FGMRES, optimization, multishooting, and trust-region methods.

Conjugate Gradient Method

Explores the Conjugate Gradient method for solving linear systems and introduces Quasi-Newton methods and rank 2 updates.

Newton's Method: Graphical Approach

Illustrates the Newton's method graphically, discussing convergence and extreme cases.

Newton's Method: Optimization Techniques

Explores optimization techniques like gradient descent, line search, and Newton's method for efficient problem-solving.

Quasi-Newton Methods

Introduces Quasi-Newton methods for optimization, explaining their advantages over traditional approaches like Gradient Descent and Newton's Method.

Solving Equations with Newton's Method

Introduces Newton's method for solving non-linear equations iteratively, highlighting its fast convergence but also its potential failure to converge in some cases.

TR global convergence (end) + CG

Covers the trust-region method and introduces the truncated conjugate gradients method.

Newton Method: Data Interpolation

Covers the Newton method for finding zeros of functions using data interpolation.

Optimization Methods

Covers optimization methods, central path algorithms, optimality conditions, and Newton's method.

Descent Methods and Newton Method with Line Search

Covers the comparison between descent methods and Newton's method, modifications, line search, and convergence analysis.

Lipschitz continuous Hessian and Newton's method

Explores the convergence of Newton's method and the CG algorithm for solving linear equations.

Newton's Method: Optimization & Indefiniteness

Covers Newton's Method for optimization and discusses the caveats of indefiniteness in optimization problems.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Solving Systems of Nonlinear Equations

Covers the Newton-Raphson method, Jacobian matrix, and iterative schemes for solving nonlinear equations.

Coordinate Descent: Efficient Optimization Techniques

Covers coordinate descent, a method for optimizing functions by updating one coordinate at a time.

Conjugate Gradient Method: Iterative Optimization

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