Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Stochastic Gradient Descent Algorithms for Resource Allocation Amrit Singh Bedi Supervisor: Dr. Ketan Rajawat DepartmentofElectricalEngineering, IndianInstituteofTechnology,Kanpur Kanpur,UttarPradesh 1/65 Subgradient descent algorithm Stochastic subgradient algorithm Incremental Stochastic subgradient algorithm Ergodic stochastic algorithm Applications in wireless communication, smart grid. Future work Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Outline Gradient descent algorithm 2/65 Stochastic subgradient algorithm Incremental Stochastic subgradient algorithm Ergodic stochastic algorithm Applications in wireless communication, smart grid. Future work Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Outline Gradient descent algorithm Subgradient descent algorithm 2/65 Incremental Stochastic subgradient algorithm Ergodic stochastic algorithm Applications in wireless communication, smart grid. Future work Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Outline Gradient descent algorithm Subgradient descent algorithm Stochastic subgradient algorithm 2/65 Ergodic stochastic algorithm Applications in wireless communication, smart grid. Future work Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Outline Gradient descent algorithm Subgradient descent algorithm Stochastic subgradient algorithm Incremental Stochastic subgradient algorithm 2/65 Applications in wireless communication, smart grid. Future work Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Outline Gradient descent algorithm Subgradient descent algorithm Stochastic subgradient algorithm Incremental Stochastic subgradient algorithm Ergodic stochastic algorithm 2/65 Future work Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Outline Gradient descent algorithm Subgradient descent algorithm Stochastic subgradient algorithm Incremental Stochastic subgradient algorithm Ergodic stochastic algorithm Applications in wireless communication, smart grid. 2/65 Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Outline Gradient descent algorithm Subgradient descent algorithm Stochastic subgradient algorithm Incremental Stochastic subgradient algorithm Ergodic stochastic algorithm Applications in wireless communication, smart grid. Future work 2/65 x is the optimization variable f(x) is the objective function g(x) is the constraint function X represents the convex domain for x Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Introduction Standard convex optimization problem minimize f(x) (1) subject to g(x)≤0 (2) x∈X 3/65 f(x) is the objective function g(x) is the constraint function X represents the convex domain for x Outline Introduction GDAlgorithm SGDMethods DDAlgorithm StochasticSGMethods IncrementalSSGAlgorithm ErgodicSSGDAlgorithm Applications References LoadSheddinginSmartGrid Introduction Standard convex optimization problem minimize f(x) (1) subject to g(x)≤0 (2) x∈X x is the optimization variable 3/65