Operator Scaling via Geodesically Convex Optimization, Invariant Theory and Polynomial Identity Testing - Yuanzhi Li
Explore geodesically convex optimization, invariant theory, and polynomial identity testing in this advanced seminar on operator scaling, featuring key theorems and proofs.
Curiosities and Counterexamples in Smooth Convex Optimization
Explore counterexamples and curiosities in smooth convex optimization, focusing on key concepts and unique aspects of this mathematical field.
A Lower Bound for Parallel Submodular Minimization
Explore lower bounds for parallel submodular minimization, examining adaptive complexity models and exponentially faster algorithms for this optimization problem.
Enlargements - A Bridge Between Maximal Monotonicity and Convexity
Explore connections between maximally monotone operators and convex functions through enlargements, offering insights into variational problems and new distance measures for point-to-set maps.
Hajime Ishihara - The Constructive Hahn Banach Theorem, Revisited
Explores constructive versions of the Hahn-Banach theorem, focusing on separation and extension theorems. Discusses geometric properties, subderivatives, and Gâteaux derivatives in functional analysis.
An Overview on a Young Research Topic - Valuations on Spaces of Functions
Explore valuations on function spaces, from convex bodies to Lipschitz and convex functions. Learn about recent classifications and advancements in this emerging mathematical field.
Geometric Probabilities and Valuation Theory
Explore applications of geometric valuation theory to probabilities and integral geometry, including Cauchy-Kubota formulas and recent findings for convex functions.
Non Linear Programming
Explore advanced optimization techniques including convex, quadratic, separable, geometric, and dynamic programming, as well as search methods and numerical integration.
Complex Monge-Ampère Operators and Functional Hermitian Intrinsic Volumes
Explore geometric construction of Monge-Ampère operators on finite convex functions, examining their properties and related valuations as functional versions of Hermitian intrinsic volumes.
Recent Advances in Valuations on Function Spaces
Explore recent developments in valuations on function spaces, focusing on convex and continuous functions, with insights into measure-valued valuations and their classifications.
Nonmonotone Forward-Backward Splitting Method for Infinite-Dimensional Optimization Problems
Explore nonmonotone forward-backward splitting for nonsmooth composite problems in Hilbert spaces, covering convergence analysis, complexity, and numerical experiments.
Stochastic Gradient Descent and Machine Learning - Lecture 1
Explore optimization methods, gradient descent, Newton's method, and convexity in machine learning. Gain insights into iterative algorithms and their applications in statistical physics and data analysis.
Gradient Descent and Stochastic Gradient Descent
Explore gradient descent and stochastic gradient descent in deep neural networks, covering convergence rates, learning rate effects, and challenges in optimization algorithms.