Mathematics of Data: Computation Role

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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.

Stochastic Optimization: Algorithms and Methods

Explores stochastic optimization algorithms and methods for convex problems with smooth and nonsmooth risks.

Primal-dual optimization: Theory and Computation

Explores primal-dual optimization, conjugation of functions, strong duality, and quadratic penalty methods in data mathematics.

Gradient Descent: Principles and Applications

Covers gradient descent, its principles, applications, and convergence rates in optimization for machine learning.

Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.

Role of Computation in Optimization

Explores the role of computation in optimization, focusing on gradient descent for convex and nonconvex problems.

Quasi-Newton Methods

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

Faster Gradient Descent: Projected Optimization Techniques

Covers faster gradient descent methods and projected gradient descent for constrained optimization in machine learning.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Proximal Gradient Descent: Optimization Techniques in Machine Learning

Discusses proximal gradient descent and its applications in optimizing machine learning algorithms.