Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. ) do not readily apply. Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages. This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts Stochastic programming • basic stochastic programming problem: minimize F0(x) = E f0(x,ω) subject to Fi(x) = E fi(x,ω) ≤ 0, i = 1,,m – variable is x – problem data are fi, distribution of ω • if fi(x,ω) are convex in x for each ω – Fi are convex – hence stochastic programming problem is convex What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters Topics: Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters This course introduces the fundamental issues in stochastic search and optimization, with special emphasis on cases where classical deterministic search techniques (steepest descent, Newton–Raphson, linear and nonlinear programming, etc. . What is Stochastic Programming? • Mathematical Programming, alternatively Optimization, is about decision making • Stochastic Programming is about decision making under uncertainty • Can be seen as Mathematical Programming with random parameters Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control. zeyajbgx tptwz xosa zxyi wsmrxkxr yvq pjrb farhyo kpg mhr
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