Optimization Basics: Linear Algebra, Analysis, Convexity

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Equivalent norms: properties and proofs

Explores equivalent norms in a vector space and their continuity properties, including proofs of norm equivalence.

Optimality of Convergence Rates: Accelerated Gradient Descent

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

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.

Proximal Gradient Descent: Optimization Techniques in Machine Learning

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

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Optimization Methods

Covers optimization methods without constraints, including gradient and line search in the quadratic case.

Gradient Descent: Principles and Applications

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

Vectors and Norms: Introduction to Linear Algebra Concepts

Covers essential concepts of vectors, norms, and their properties in linear algebra.

Singular Values and Norms: Understanding Linear Maps with SVD

Explores singular value decomposition and its role in understanding linear maps.

Orthogonality and Least Squares Method

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.