Erwin Schrödinger International Institute for Mathematics and Physics (ESI) Courses

Sum-of-Minimum Model: Joint Optimization of Specialized Models for Heterogeneous Data

Explore joint optimization of specialized models for heterogeneous data using the sum-of-minimum approach. Learn algorithm design, performance bounds, and applications in various machine learning tasks.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Kurdyka-Łojasiewicz Exponent for Hadamard-Difference-Parameterized Models

Explore Kurdyka-Łojasiewicz exponents in L1-regularized optimization, focusing on Hadamard difference parametrization and its impact on local convergence rates of gradient methods.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Toward a Grand Unified Theory of Accelerations in Optimization and Machine Learning

Explore acceleration mechanisms in optimization and machine learning, aiming to unify diverse approaches for a comprehensive mathematical theory.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Semi-Newton Method in Difference Programming

Explore a novel Newton-type algorithm for nonsmooth optimization problems, focusing on difference programming and its applications in structured optimization and practical problem-solving.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Revisiting Inexact Fixed-Point Iterations for Min-Max Problems - Stochasticity and Cohypomonotonicity

Explore advanced optimization techniques for constrained min-max problems, focusing on inexact fixed-point iterations and stochastic algorithms for nonconvex-nonconcave scenarios.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Kato Meets Bakry-Émery: Curvature Conditions in Riemannian Geometry

Explore the relationship between Bakry-Émery curvature-dimension and Kato condition on Ricci curvature, uncovering insights on Kato limit spaces and Riemannian manifolds.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

Strong Convergence of Inertial Algorithms via Tikhonov Regularization

Explore inertial algorithms with Tikhonov regularization for optimization problems, examining strong convergence to minimum norm solutions and fast convergence rates for objective function values.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

The First Optimal Distributed SGD in the Presence of Data, Compute and Communication Heterogeneity

Explore optimal time complexities for parallel optimization methods with heterogeneous data, compute, and communication. Gain insights into efficient distributed SGD algorithms.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Optimization of Functions with Low Effective Dimensionality

Explore optimization techniques for functions with low effective dimensionality, focusing on random and deterministic subspace methods for nonconvex problems and efficient subspace learning.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Bilevel Optimization Problems: Algorithms and Theory

Explore recent developments in bilevel optimization algorithms, their theoretical analysis, and challenges in machine learning and data science applications.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Hessian-Aware Stochastic Differential Equation Modeling of SGD

Explore a novel SDE model for SGD that incorporates Hessian information, improving accuracy in capturing escaping behaviors and achieving exact recovery for quadratic objectives.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Stochastic Algorithms for Constrained Continuous Optimization

Explore stochastic-gradient-based algorithms for constrained continuous optimization, focusing on interior-point and sequential-quadratic-programming methods with convergence guarantees and practical applications.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization

Explore sample size estimates for risk-neutral semilinear PDE-constrained optimization using SAA approach, covering nonasymptotic analysis and numerical illustrations.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

A New Derivative-Free Method Using an Improved Under-Determined Quadratic Interpolation Model

Explore a novel derivative-free optimization method using improved under-determined quadratic interpolation, considering trust-region iteration properties and model optimality.

• YouTube
• 23 minutes
• Self-Paced
• Free Video