Conjugate Gradient Optimization

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Convex Optimization: Gradient Algorithms

Covers convex optimization problems and gradient-based algorithms to find the global minimum.

Conjugate Gradient Method

Covers the Conjugate Gradient method for solving linear systems efficiently.

Momentum methods and nonlinear CG

Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

Quadratic Forms and Symmetric Matrices

Explores examples of algebraic quotients using invariance maps and discriminant.

Optimization Methods in Machine Learning

Explores optimization methods in machine learning, emphasizing gradients, costs, and computational efforts for efficient model training.

Iterative Methods for Linear Equations

Explores iterative methods for linear equations, including Jacobi and Gauss-Seidel methods, convergence criteria, and the conjugate gradient method.

Iterative Methods for Linear Equations

Introduces iterative methods for linear equations, convergence criteria, gradient of quadratic forms, and classical force fields in complex atomistic systems.

Lyapunov Stability Theory: Energy Functions and Stability Analysis

Covers Lyapunov stability theory, energy functions, positive-definite matrices, and system stability analysis through examples and theorems.