Descent Methods and Newton Method with Line Search

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Linear Systems: Iterative Methods

Explores linear systems and iterative methods like gradient descent and conjugate gradient for efficient solutions.

Iterative Methods for Linear Equations

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

Gradient Descent

Covers the concept of gradient descent in scalar cases, focusing on finding the minimum of a function by iteratively moving in the direction of the negative gradient.

Quasi-Newton Methods

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

Newton's Method: Optimization & Indefiniteness

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

Coordinate Descent: Efficient Optimization Techniques

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

Newton's Method: Optimization Techniques

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

Newton Method: Convergence and Quadratic Care

Covers the Newton method and its convergence properties near the optimal point.

Linear Systems: Convergence and Methods

Explores linear systems, convergence, and solving methods with a focus on CPU time and memory requirements.

Optimality of Convergence Rates: Accelerated Gradient Descent

Explores the optimality of convergence rates in convex optimization, focusing on accelerated gradient descent and adaptive methods.