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NTHRYS › PhD Assistance › Mathematical Optimization

Mathematical Optimization

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Mathematical Optimization

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Convex Optimization Theory and Algorithms
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Non-Convex Optimization Landscapes
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Stochastic Gradient Descent Methods
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Distributed Optimization Algorithms
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Second-Order Optimization Methods
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Integer and Combinatorial Optimization
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Linear Programming and Polyhedral Theory
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Semidefinite Programming Relaxations
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Variational Inequalities and Monotone Operators
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Proximal Methods and Operator Splitting
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Frank-Wolfe and Conditional Gradient Methods
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Accelerated Optimization Methods
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Online Learning and Regret Bounds
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Bandit Optimization and Exploration
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Gradient-Free and Black-Box Optimization
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Bayesian Optimization and Gaussian Processes
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Reinforcement Learning Control Problems
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Robust Optimization and Uncertainty
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Bilevel Optimization Problems
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Multi-Objective Optimization Pareto Methods
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Network Flow and Transportation Problems
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Facility Location and Clustering
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Scheduling and Resource Allocation
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Machine Learning Feature Selection
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Deep Neural Network Training Optimization
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Tensor and Low-Rank Matrix Optimization
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Matrix Completion and Missing Data
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Compressed Sensing and Sparse Recovery
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Online Convex Optimization Games
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Nash Equilibrium and Variational Approaches
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Supply Chain and Logistics Optimization
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Power System and Energy Optimization
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Portfolio Optimization and Finance
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Derivative-Free Trust Region Methods
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Parameter Tuning and Hyperparameter Optimization
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Quantum Optimization Algorithms
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Convergence Rate Analysis and Complexity
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Federated Learning and Privacy-Preserving Optimization
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Neural Architecture Search Optimization
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Smooth and Non-Smooth Analysis
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Variational Methods in Physics
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Data-Driven and Learning-Augmented Optimization
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Graph and Network Optimization
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Stochastic Optimization with Constraints
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Coordinate Descent and Decomposition Methods
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Saddle Point and Minimax Optimization
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Generative Adversarial Network Training
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Constraint Qualification and Duality Theory
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Mixed-Integer Nonlinear Programming
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Augmented Lagrangian Methods
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Manifold Optimization and Riemannian Geometry
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Zeroth-Order Optimization and Function Evaluations
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Variance Reduction Techniques in Stochastic Methods
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Asynchronous Distributed Optimization Networks
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Mirror Descent and Bregman Divergences
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Decentralized Consensus Optimization Methods
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Hardness of Approximation in Optimization
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Submodular Optimization and Greedy Algorithms
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Stochastic Mirror Descent and Online Games
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Extragradient Methods and Monotone Inclusion
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Zeroth-Order Momentum and Acceleration
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Optimization Under Differential Privacy Constraints
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Portfolio Theory and Mean-Variance Optimization
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Cutting Plane Methods and Ellipsoid Algorithms
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Conic Programming and Self-Concordant Functions
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Derivative-Free Optimization with Surrogate Models
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Frank-Wolfe Variants and Linear Minimization Oracle
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Primal-Dual Optimization and Duality Gaps
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Nonconvex Landscape Characterization and Geometry
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Cyclic and Block Coordinate Descent Methods
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Trust Region Methods and Newton Steps
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Projected Gradient Descent with Constraints
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Conditional Expectation and Variance in Sampling
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Game Theory and Multi-Agent Optimization
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Sparse Optimization and L0 Minimization
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Time-Varying and Non-Stationary Optimization
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Greedy Algorithms and Approximation Guarantees
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Convex Relaxations and SDP Hierarchies
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Dual Averaging and Mirror Maps Theory
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Parallel Optimization and Speedup Analysis
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Proximal Alternating Linearized Method
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Warm Starting and Transfer Learning in Optimization
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Projection-Free Methods and Conditional Gradients
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Quasi-Newton Methods and Hessian Approximation
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Optimization with Implicit Regularization
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Compositional Optimization and Nested Structures
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Stochastic Optimization under Heavy Tails
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Gradient Descent Escape from Saddle Points
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Continuous Relaxations of Discrete Programs
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Convex Geometry and Volume Estimation
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Stochastic Variance-Reduced Methods with Momentum
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Parametric and Sensitivity Analysis Optimization
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Gradient Tracking and Gossip Algorithms
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Conditional Gradient Methods with Acceleration
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Optimization with Monotone and Maximal Operators
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Consensus and Distributed Machine Learning
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Stochastic Optimization Lower Bounds
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Splitting Methods and Operator Theory
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Structured Sparsity and Group Norms
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Optimal Transport and Wasserstein Distances
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Adaptive Learning Rate Scheduling Optimization
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Composite Optimization with Nonsmooth Penalties
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Asynchronous Parallel Optimization Convergence
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Conditional Value-at-Risk Optimization Applications
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Derivative-Free Evolutionary Algorithm Analysis
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Zeroth-Order Optimization for High Dimensions
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Decentralized Consensus-Based Optimization Networks
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Monotone Inclusion and Fixed Point Methods
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Primal-Dual Splitting Schemes Convergence
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Conic Programming and Cone Geometry
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Submodular Function Maximization Approximation
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Reformulation-Linearization Technique Development
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Cutting Plane Methods and Branch-and-Cut
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Penalty Methods and Exact Penalization
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Natural Gradient and Riemannian Optimization
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Oracle-Based Lower Bounds Complexity Theory
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Momentum-Based Acceleration Mechanisms Analysis
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Robust Optimal Transport and Wasserstein
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Trust Region Methods Globalization Strategies
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Alternating Direction Method of Multipliers Variants
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Constraint Reduction and Infeasibility Detection
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Stochastic Dual Averaging Online Algorithms
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Nonconvex Landscape Escaping Local Minima
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First-Order Methods for Minimax Optimization
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Sketching and Randomized Dimensionality Reduction
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Coordinate Minimization and Block Updates
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Nonlinear Programming Constraint Qualification
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Optimistic Gradient Methods Best Possible Rates
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Stochastic Variance-Reduced Gradient Methods
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Extragradient and Forward-Backward Variants
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Adaptive Subgradient Methods Convergence Guarantees
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Dual Decomposition and Lagrangian Relaxation
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Approximate Message Passing Algorithm Analysis
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Smoothing Techniques for Nonsmooth Problems
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Majorization-Minimization Algorithms Convergence
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Nonconvex Regularized Regression Phase Transitions
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Implicit Differentiation for Optimization Layers
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Online Gradient Descent Dynamic Regret Analysis
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Composite Convex Function Optimization Acceleration
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Sparse Principal Component Analysis Optimization
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Sequential Convex Programming Methods Development
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Optimal Control and Trajectory Optimization Methods
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Graph Neural Network Training Optimization
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Randomized Block Coordinate Descent Rates
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Subsampled Newton Methods Large-Scale Learning
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Exponential Family and Natural Parameter Estimation
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Inexact Gradient Descent Perturbation Analysis
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Variance Reduction in Stochastic Optimization
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Asynchronous Parallel Optimization Methods
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Manifold Optimization and Riemannian Methods
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Conditional Gradient Dynamics and Flows
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Monotone Inclusion Problems and Splitting
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Finite-Time Convergence Rate Analysis
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Zeroth-Order Optimization and Gradient Estimation
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Proximal Point Algorithms and Regularization
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Adaptive Learning Rate and Preconditioning
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Compositional Optimization and Nested Functions
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Decentralized Consensus Optimization Networks
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Non-Ergodic and Last-Iterate Convergence
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Implicit Differentiation and Implicit Bias
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Hamiltonian and Symplectic Optimization Dynamics
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Heavy Ball and Momentum Acceleration Methods
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Dual Averaging and Mirror Descent Methods
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Submodular Function Maximization Algorithms
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Constraint Handling and Active Set Methods
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Regularized Empirical Risk Minimization Theory
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Wasserstein Gradient Flows and Optimal Transport
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Differential Privacy in Optimization Algorithms
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Decoupled and Separable Optimization Structures
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Smoothing and Regularization Techniques Optimization
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Universal Gradient Methods and Adaptivity
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Prox-Linear and Composite Gradient Methods
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Stochastic Approximation and Recursive Algorithms
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Localization and Local Convergence Analysis
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Extragradient and Extrapolation Methods
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Sketching and Dimensionality Reduction Optimization
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Projected and Constrained Optimization Dynamics
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Averaged Gradient and SAG Methods
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Interior Point and Barrier Methods Modern Theory
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Stochastic Variational Inequalities Solutions
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Escaping Saddle Points in Non-Convex Optimization
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Gradient Clipping and Norm-Constrained Optimization
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Distributed Gradient Compression and Quantization
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Free Lunch Theorems and Lower Bounds
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Orthogonal and Structured Matrix Optimization
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Implicit Regularization and Generalization
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Consensus-Based Sampling and Derivative-Free Methods
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Nonlocal Operators and Fractional Calculus Optimization
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Continuous-Time Optimization and ODEs
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Inexact Proximal and Approximate Methods
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Gradient Tracking and Dual Correction Methods
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Submodular Optimization and Greedy Approximations
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Distributed Federated Learning and Decentralized Training
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Polyak-Lojasiewicz Condition and Quadratic Growth
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Implicit Differentiation and Bilevel Gradient Computation
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Peer-to-Peer and Gossip Optimization Networks
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Stochastic Variance-Reduced Methods and Catalyst Acceleration
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Monotone Operator Splitting and Proximal Algorithms
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Bilevel and Hierarchical Game-Theoretic Learning
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Zeroth-Order Optimization for Black-Box Functions
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Optimal Transport and Wasserstein Distance Methods
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