Two approaches to handling uncertainty. Consider an LP:

\begin{align} &\min c^{T}x \\ &s.t. a_{i}^{x} \leq b_{i} \end{align}

what if our constraints are uncertain. Both of these reduce to an SOCP. See slides.

Deterministic Worst-Case

\begin{align} &\min c^{T}x \\ &s.t.\ a_{i}^{T} x \leq b_{i}, \forall a_{i} \in \epsilon_{i} \end{align}

Stochastic

\begin{align} &\min c^{T}x \\ &s.t.\ \text{prob}\qty(a_{i}^{T} x \leq b_{i}) \geq \eta, i = 1 \dots m \end{align}

\begin{align} &\min c^{T}x \\ &s.t.\ x_1 F_1 + x_2 F_2 + \dots + x_{n} F_{n} + G \preceq 0 \\ & Ax = b \end{align}

Key Sequence

Notation

New Concepts

• Disciplined Convex Programming
• more ways of checking convexity
  • perspective
  • conjugate function
• quasiconvex function
• optimization (math)
  • convex problems
  • feasible
  • optimal value and locally optimal
• special convex problems
  • Linear Program

Important Results / Claims

• Cash Flow Return Tracking
• properties of quasiconvex functions

Questions

Interesting Factoids

Fun example

Key Sequence

Notation

New Concepts

• Types of convex problems
  • Linear Program
  • Quadratic Program
  • Quadratically constrained quadratic program
  • Second-order cone programming
  • Robust Optimization
  • Semidefinite Program
  • Convex Problem Hiearchy
• problem transformation

Important Results / Claims

Questions

Interesting Factoids

Key Insights

1. Does China have a modern form of government?
2. China’s National Government as a Hierarchy: is it centralized? Meritocratic?

Forms of Government

1. Modern Government Model (“European Model”—Enlightenment English/Scottish/French): state should adjudicate interests in a fair and legitimate fashion
   • US Government Model: hybrid, constitutional, late 18th entry design (i.e. “government is designed to stop things”)
2. Alternative Model (“Developer Model”): State’s purpose is to push national progress through economic and military strength (i.e. “the government pushes things forward)
   • China
   • Axis Powers

Modern Government

We typical define a modern government as a liberal democratic government. But China’s system is in some sense much newer than liberal democracy—invented by the Soviets.