Global Optimization for Cardinality-Constrained Minimum Sum-of-Squares Clustering via Semidefinite Programming
Explore global optimization techniques for cardinality-constrained minimum sum-of-squares clustering using semidefinite programming, focusing on exact algorithms and state-of-the-art approaches.
The Effect of Parametrization on Nonconvex Optimization Landscapes - Seminar
Explore the relationship between optimization landscapes in parametrized problems. Gain insights into applications like low-rank matrix optimization, semidefinite programming, and neural network training.
Goemans-Williamson: Rounding the Max-Cut SDP - Lecture 20a of CS Theory Toolkit
Efficient algorithm for approximating maximum graph cuts using semidefinite programming and randomized rounding, with guaranteed performance ratio of 0.878.
The SDP Relaxation for Max-Cut - Lecture 19b of CS Theory Toolkit
Explore SDP relaxation for Max-Cut, transforming a quadratic program into a semidefinite program solvable by the Ellipsoid Algorithm. Part of CMU's graduate-level CS Theory Toolkit course.
Modular Forms by Mahesh Kakde
Comprehensive exploration of modular forms, covering definitions, properties, and applications. Delves into Eisenstein series, theta functions, and related mathematical concepts for advanced learners in number theory.
Fast Semidefinite Programming for Differentiable Combinatorial Optimization
Explore advanced techniques in semidefinite programming for combinatorial optimization, focusing on fast and differentiable methods presented by Carnegie Mellon expert Zico Kolter.
How Do Exponential Size Solutions Arise in Semidefinite Programming?
Explore the prevalence and implications of exponential size solutions in semidefinite programming, their impact on feasibility determination, and strategies for efficient representation.
Sensor Network Localization with Noisy Distance Measurements
Explore sensor network localization techniques using noisy distance measurements, including EDM problems, semidefinite programming, and nonlinear least-squares optimization for accurate node positioning.
Distance Matrix Completions
Explores partial matrices, completions, and distance matrices, focusing on characterizing patterns for distance completable partial matrices and their geometric implications.
Auxiliary Functionals - A Path to Solving the Problem of Turbulence
Explore innovative approaches to solving turbulence in fluid dynamics using auxiliary functionals and sum-of-squares polynomial optimization, with applications to Kuramoto-Sivashinsky and Navier-Stokes equations.
Linear Programming and Semidefinite Programming in Coding Theory - An Incomplete Overview
Explore linear programming in coding theory, including MRRW and Levenshtein bounds, spherical codes, and connections to combinatorial objects. Discover recent advances in equiangular lines and energy bounds.
Exploiting Sparsity in Polynomial Optimization - Lecture 1
Explore sparsity exploitation techniques in polynomial optimization, focusing on advanced mathematical concepts and practical applications.
Monogamy of Highly Symmetric States in Quantum Entanglement
Explore entanglement limits in highly symmetric quantum states on complete graphs, using semidefinite programming and representation theory to solve long-standing problems.
An SU(2)-symmetric Semidefinite Programming Hierarchy for Quantum Max Cut
Explore advanced quantum physics through SU(2)-symmetric semidefinite programming hierarchies, focusing on Quantum Max Cut problem and its applications in approximating extremal energy states of local Hamiltonians.
Explicit SoS Lower Bounds from Small-Set High Dimensional Expanders
Explores explicit CSPs hard for Sum-of-Squares hierarchy using small-set high dimensional expanders, introducing new isoperimetric inequality for Square Cayley Complexes to construct optimally hard XOR-families.
Quantum Algorithms for Optimization - Quantum Colloquium
Explore quantum algorithms for optimization, including discrete and continuous problems, with insights on potential speedups and limitations in quantum computing applications.
Contracted Quantum Eigensolver for the Quantum Simulation of Many-Electron Systems
Explore a novel quantum algorithm for many-body systems, comparing it to existing methods and demonstrating its advantages in molecular simulations and quantum computing applications.
Robust Regression by Purushottam Kar
Explore robust regression techniques for learning and estimation in algorithms and optimization, focusing on practical applications and theoretical foundations.
Characterising Quantum Correlations of Fixed Dimension
Explores semidefinite programming for quantum correlations, improving approximation algorithms for two-player free games with quantum assistance using entropy inequalities and de Finetti theorems.
Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions
Explore neural set function extensions for integrating discrete functions into neural networks, focusing on continuous domain extensions and high-dimensional representations for combinatorial optimization.
Packing Points in Projective Spaces
Explore optimal point arrangements in projective spaces, surveying current research and open problems in this fundamental area of metric geometry with applications in digital communication.