现代商业决策环境日趋复杂多变，如何在错综复杂的不确定性环境下理性的看待风险与机遇，并运用正确的量化工具来优化决策者的收益结构至关重要。 本课程基于各类实际决策问题为背景，全面介绍处理不确定性决策的多种建模技术以及优化方法。本课程的特色在于将行为、风险决策理论、随机优化以及鲁棒优化方法的前沿进展整合为一体，在更全面深刻的框架下展示不确定性决策的本质及其建模与优化工具。通过本课程的学习，学生预期能够掌握几类基本的决策模型及其优化方法以满足不同的实际建模需求，理解各类模型之间的关联以及它们在处理不确定性的局限性，并能运用这些模型工具解决实际问题。

Lecture 1: Introduction to Optimization under Uncertainty
Introduction to the course; utilities and decision; optimization problems and modeling; some examples
Lecture 2: Basis of Convex analysis
Convex set and cone; Convex functions; other preliminaries
Lecture 3: Basis of Linear Optimization
Linear program; linear conic programs; duality theory; optimization tools
Lecture 4: Tutorial I
Lecture 5: Ambiguity, Risk and Uncertainty: Part I
Differences and connections among ambiguity, risk and uncertainty; evidences from behavior finance; modeling the ambiguity
Lecture 6: Ambiguity, Risk and Uncertainty: Part II
Identifying the invariants; choosing the right utility; decision-makers’ perception
Lecture 7: Measuring the risk
Coherent risk measures; the bad news on Value-at-Risk; examples
Lecture 8: Tutorial II
Lecture 9: Robust Optimization (RO): Part I
Uncertainty set: Interval, polyhedron and ellipsoid; robust counterpart;          good news & bad news of RO; some examples
Lecture 10: Robust Optimization and Risk Measure
Robust counterpart risk measure; Connections between RCRM and other risk measures; examples
Lecture 11: Probabilistic Optimization: Part I
Chance constraint program; an example: portfolio optimization; sample average approximation
Lecture 12: Probabilistic Optimization: Part II
CVaR Approximation; robust counterpart approximation; joint chance constraint approximation 
Lecture 13: Tutorial III
Lecture 14: Two-Stage Stochastic Programming: Part I
Facility-Location planning; capacity planning; newsvendor problems
Lecture 15: Two-Stage Stochastic Programming: Part II
Deterministic equivalent formulation; valuation of random solution; expected value of perfect information
Lecture 16: Two-Stage Stochastic Programming: Part III
Sample average approximation; L-shaped solution methods; some examples 
Lecture 17: Adaptive Optimization
Two-stage SP as a special case; adjustable robust models; adaptive optimization with ambiguity
Lecture 18: Tutorial IV

1.	A. Ben-Tal, L. El Ghaoui, and A. Nemirovski, Robust Optimization, Princeton Series in Applied Mathematics, Princeton University Press, 2009.
2.	J.R. Birge and F. V. Louveaux. Introduction to Stochastic Programming, 2nd Edition, Springer-Verlag, New York, 2010.
3.	S Wang, Lecture Notes for Decision and Optimization under Uncertainty, 2016.