week 13

\(\def\Real{\mathbb{R}}
\def\Comp{\mathbb{C}}
\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\def\Fun{\mathbf{Fun}}
\def\e{\mathbf{e}}
\def\f{\mathbf{f}}
\def\bv{\mathbf{v}}
\)

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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