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.
Provable Submodular Function Minimization via Fujishige Wolfe Algorithm
Explore submodular function minimization through the Fujishige-Wolfe algorithm, analyzing its convergence and implications for combinatorial optimization.
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.
Large Scale Machine Learning and Convex Optimization - Lecture 1
Explore advanced stochastic optimization techniques for large-scale machine learning, including novel Newton-based algorithms and hybrid approaches that achieve improved convergence rates and efficiency.
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.
Can Learning Theory Resist Deep Learning? - Francis Bach, INRIA
Exploring global convergence of gradient descent in non-convex optimization for deep learning, highlighting challenges in bridging theory and practice in machine learning algorithms.
Optimization: Higher-order Methods - Part 2
Explore advanced optimization techniques and higher-order methods for fast algorithms, focusing on data structures and their applications in algorithmic efficiency.
Optimization: Higher-order Methods - Part 1
Explore advanced optimization techniques using higher-order methods, focusing on theoretical foundations and practical applications in algorithm design and data structures.
Optimization: First-order Methods - Part 2
Explore advanced first-order optimization techniques, focusing on accelerated gradient methods and their applications in solving complex algorithmic problems.
Optimization: First-order Methods - Part 1
Explore first-order optimization methods with Alina Ene, focusing on fundamental techniques and algorithms for efficient problem-solving in data structures and algorithm design.
Barycenters and a Law of Large Numbers in Gromov Hyperbolic Spaces
Explore barycenters in Gromov hyperbolic spaces, examining contraction properties and a law of large numbers for convex optimization applications in metric spaces.
A Stochastic Newton Algorithm for Distributed Convex Optimization
Explore a novel stochastic Newton algorithm for distributed convex optimization, reducing communication rounds while maintaining performance. Gain insights into convergence guarantees and practical applications.
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.
Recent Progress on Submodular Function Minimization
Explore recent advancements in submodular function minimization algorithms, leveraging convex optimization methods to address open questions and improve efficiency in discrete optimization.
High-Dimensional PDEs, Tensor Networks, and Convex Optimization
Explore innovative computational methods for high-dimensional PDEs using tensor networks and convex relaxations, addressing the curse of dimensionality with low-order statistics approximations.
Information Complexity of Mixed-Integer Convex Optimization
Explore information complexity in mixed-integer convex optimization, including oracle-based bounds and partial first-order information impacts, with insights from Professor Amitabh Basu.
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.
Progressive Decoupling of Dynamics in Convex Optimal Control
Explore progressive decoupling in convex optimization for optimal control, connecting classical calculus of variations with modern convex analysis and duality concepts.