**Matrix scaling in linear and convex programming**

*Bahman** Kalantari*

Diagonal scaling in linear
programming became a prominent technique with

the announcement of Karmarkar
algorithm. In the context of nonnegative

matrices, doubly stochastic diagonal scaling
had been a subject of

research for more than half a century prior
to the emergence of

interior-point methods for LP. The link between
these two otherwise

disjoint fields is diagonal scaling of a
symmetric positive semidefinite

matrix into a doubly quasi-stochastic
matrix. The complexity of the

latter problem was studied by Khachiyan and Kalantari who also
used it

to give, as a by-product, a simple
unique path-following algorithm for

LP. In this talk not only do we wish to
promote and justify the

significance and relevance of positive semidefinite matrix scaling in

linear programming, but of its
generalization in semidefinite as well

as self-concordant programming. These
are from the point of view of

pedagogical, foundational, theoretical,
algorithmic, and possibly even

practical considerations.