\(\def\Real{\mathbb{R}}

\def\Comp{\mathbb{C}}

\def\Rat{\mathbb{Q}}

\def\Field{\mathbb{F}}

\def\Fun{\mathbf{Fun}}

\def\e{\mathbf{e}}

\def\f{\mathbf{f}}

\def\bv{\mathbf{v}}

\)

#### Interior point methods

Logarithmic barriers. Central path. Convergence and quality of solution estimates from duality. (Boyd, chapt.11).

#### Ellipsoid method

(Use Boyd’s notes).

#### Sample problems

- Find the central path for the problem

\[

\begin{array}{rl}

ax+by&\to\min, \mathrm{\ subject\ to}\\

x\geq&0\\

y\geq&0\\

x+y\leq&1\\

\end{array}

\]

for different \(a,b\) (for example, \(a=3,b=5\)).

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