Lectures related to Optimization problems

Covers the analysis of stationary points in functions, focusing on optimization methods.

Optimization Methods: Lagrange Multipliers

Covers advanced optimization methods using Lagrange multipliers to find extrema of functions subject to constraints.

Discusses Lagrange multipliers for optimizing functions subject to constraints, with examples illustrating their application.

Lagrange Multipliers

Covers Lagrange multipliers for optimizing functions subject to constraints on surfaces.

Optimization Methods: Convergence and Trade-offs

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

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Local Extrema of Functions

Discusses local extrema of functions in two variables around the point (0,0).

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Gradient Descent Methods: Theory and Computation

Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.

Extreme Values and Constraints

Explores extreme values, constraints, Riemann's integral interpretation, and volume calculations of parallelipipeds in mathematics.

Convex Functions

Covers the definition of convex functions and their properties in optimization.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Optimization with Lagrange Multipliers

Covers advanced optimization techniques using Lagrange multipliers to find extrema of functions subject to constraints.

Minimization of functions

Explores techniques for minimizing functions and finding critical points.

Primal-dual Optimization III: Lagrangian Gradient Methods

Explores primal-dual optimization methods, emphasizing Lagrangian gradient techniques and their applications in data optimization.

Optimization: Extrema of Functions

Covers the optimization of functions, focusing on finding the maximum and minimum values.

Geodesic Convexity: Basic Facts and Definitions

Explores geodesic convexity, focusing on properties of convex functions on manifolds.

Non-Convex Optimization: Techniques and Applications

Covers non-convex optimization techniques and their applications in machine learning.

Convexity and Optimization

Explores convexity, optimization, and critical points in mathematical functions using the second derivative.