Lectures related to Optimality Conditions: Sufficient Optimality Conditions

Covers Fermat's theorem, necessary optimality conditions, convexity, and eigenvalue curvature in optimization.

Concavity and Convexity: Analysis of Functions

Explores concavity, convexity, critical points, and singularities in functions.

Convexity and Concavity: Inflection Points, Taylor Expansion, and Darboux Sums

Explores inflection points, convexity, concavity, and asymptotes in functions, with examples and applications.

Covers the concept of continuous derivatives and their application in analyzing functions and determining critical points.

Optimization Basics

Introduces optimization basics, covering logistic regression, derivatives, convex functions, gradient descent, and second-order methods.

Convexity and Concavity

Covers the concepts of convexity and concavity in functions with examples.

Convexity and Optimization

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

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Extrema of Functions

Covers the discussion of local extrema, concavity, convexity, and inflection points in functions.

Optimal Transport: Rockafellar Theorem

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Convexity Study and Limiting Developments

Explores convexity, concavity, and limiting developments for functions, emphasizing extrema and derivative properties.

Convexity: Functions and Global Minima

Explores convex functions, global minima, and their relationship with differentiability.

Convex Optimization: Convex Functions

Covers the concept of convex functions and their applications in optimization problems.

Optimization Techniques: Convexity in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity and its implications for efficient problem-solving.

Partial Derivatives: Gradient and Theorem of Mean Value

Introduces the gradient concept and the Theorem of Mean Value for functions in several variables.

Rolle's and Mean Value Theorem

Covers higher derivatives, local extrema, and the application of Rolle's and Mean Value Theorems.

Inflection Points

Explores inflection points in functions, emphasizing the role of the second derivative.

Gradient Descent: Optimization

Explains gradient descent for optimization and how to find the direction towards the solution by minimizing distances.

Optimization Techniques: Convexity and Algorithms in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity, algorithms, and their applications in ensuring efficient convergence to global minima.