IF \(C\) and \(D\) are non-empty disjoint \(C \cap D = \emptyset\), and \(C\) and \(D\) are convex sets, \(\exists a \neq 0\) such that:

\begin{equation} a^{T} x \leq b, x \in C \end{equation}

\begin{equation} a^{T}x \geq b, x \in D \end{equation}

The hyperplane:

\begin{equation} \qty {x \mid a^{T} x = b} \end{equation}

separates \(C, D\) such that \(a^{T}x \geq b, a^{T}x \leq b\).

Key Sequence

Notation

New Concepts

• optimization (math)
  • convex optimization
  • non-linear optimization
• convex sets

Important Results / Claims

Questions

Interesting Factoids

::PROPERTIES: :ID: 5440B722-5661-4B1A-99D2-B6D48481DDA2 :END:

Potential measures of China’s decline:

• purchasing power is not as high even if its a huge economy
• incomes are not rising as fast as they did before
• model of property-driven growth

influences

• China’s working age productivity is shrinking
• China’s total productivity has decreased
• ROI from Chinese companies have declined
• …and thus foreign direct investment is reversing

bailouts

Unlike the US financial crisis, when big companies go bust, China didn’t bail out companies except to finish already-purchased homes.

four pillars of medical ethics

• beneficence: act in the best interest of the patience
• non-maleficence: do no harm
• autonomy: respect the right of people to make decisions for themselves
• justice: seek fairness with what we do

…on children

• autonomy is very adult centric… “substituted judgment is hard”
• altruistic surrogacy: act in the children’ best interest
• altruism: doesn’t require the consent / knowledge of others + doing something for someone else

ethical equivalency

Agreeing to withhold a treatment is equivalent to agreeing to stop it.