Standard linear programming may be thought of as
optimizing a linear cost function over the intersection
of an affine subspace and the cone of nonnegative
vectors. In conic linear programming the cone
of nonnegative vectors may be replaced by various
other closed convex cones, like the second order
cone (in it, the first coordinate bounds the norm
of the vector of the remaining coordinates) or
the cone of (symmetric) positive semidefinite
matrices. For the latter two examples there also
exist rather robust algorithmic methods to solve
these optimization problems efficiently and this
opens up a whole new world of important applications.
The course offers a brief introduction to theory,
algorithms and applications of conic linear programming.
The following two papers would each be suitable for
a group of 3-4 students to read and prepare a
presentation on (please try to understand and
explain the applications, not the theory and
algorithms):
http://stanford.edu/~boyd/papers/pdf/socp.pdfhttps://web.stanford.edu/~boyd/papers/pdf/semidef_prog.pdf
