Юрий дорн
Оптимизация и приложения
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О курсе
Этот курс посвящен оптимизационным задачам, включающим неопределенность в данных. Этот раздел оптимизации очень богат на приложения: финансы, логистика и оптимизация Supply Chain, статистическое оценивание и другие.
В этом курсе мы разберем основные техники стохастической и робастной оптимизации.
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Команда курса
Юрий Дорн
Лектор
Григорий Малиновский
Ассистент
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Программа
Stochastic and Robust Optimization
  • Introduction
  • Application examples
  • Examples: Two-stage and multistage stochastic models
  • Robust Optimization approach
Two-Stage and Multistage problems
  • Linear two-stage problems
  • Polyhedral two-stage problems
  • General two-stage problems
  • Nonanticipativity
  • Multistage problem: formulation
  • Duality
Optimization Problems with Probabilistic Constraints
  • Convexity in Probabilistic Optimization
  • Separable Probabilistic Constraints
  • Optimization Problems with Nonseparable Probabilistic Constraints
  • Robust Counterpart Approximation of Scalar Chance Constraints
Robust Counterparts approximations of scalar chance constraints
  • Globalized robust counterparts of uncertain LO problems
  • Robust CR of a Safe Convex Approximations to a Scalar Chance Constraint
  • Bernstein Approximation of a Chance Constraint
  • From Bernstein Approximation to CVaR and back
  • Majorization
Uncertain Conic Optimization
  • Uncertain Conic Optimization: Preliminaries
  • Robust counterpart of uncertain Conic Problem: Tractability
  • Safe Tractable Approximations of RC of Uncertain Conic Inequalities
Uncertain Conic Quadratic Problems with tractable RCs
  • Scenario Uncertainty
  • Simple Interval Uncertainty
  • Unstructured Norm-Bounded Uncertainty
  • Convex Quadratic Inequality with Unstructured Norm-Bounded Uncertainty
  • CQI with Simple Ellipsoidal Uncertainty
  • Approximating RCs of Uncertain Conic Quadratic Problems
Uncertain Semidefinite Problems with tractable RCs
  • Uncertain Semidefinite Problems
  • Tractability of RCs of Uncertain Semidefinite Problems
  • Approximating RCs of Uncertain Semidefinite Problems
Robust Classification and Estimation
  • Robust SVM
  • Robust Classification and Regression
  • Affine Uncertainty Models
  • Random Affine Uncertainty Models
Statistical Inference
  • Statistical Properties of Sample Average Approximation Estimators
  • Stochastic Generalized Equations
  • Monte Carlo Sampling Method
  • Quasi-Monte Carlo Methods
  • Variance Reduction Techniques
Statistical Inference II
  • Chance Constrained Problems [Monte Carlo Sampling Approach]
  • Multistage Stochastic Programming via SAA method
  • Stochastic Approximation Method
  • Stochastic Dual Dynamic Programming Method
Risk Averse Optimization
  • Mean-Risk Models
  • Coherent Risk Measures
  • Ambiguous Chance Constraints
Risk Averse Optimization II
  • Optimization of Risk Measures
  • Statistical Properties of Risk Measures
  • Multistage Risk Averse Optimization
Robust Markov Decision Processes
  • Markov Decision Processes
  • The Robust MPD Problems
  • The Robust Bellman Recursion on Finite Horizon
Robust Adjustable Multistage Optimization
  • Adjustable Robust Optimization: Motivation
  • Adjustable Robust Counterpart
  • Affinely Adjustable Robust Counterparts