Computing Integral Solutions for Semidefinite Programs

programming in which the positive orthant is replaced by the cone of
symmetric positive semidefinite matrices. In the talk, I will give
an extension of Lenstra's theorem on the polynomial-time solvability
of integer linear programming in fixed dimension to integer semidefinite
programming. In fact, I will consider the more general problem of
computing integral points in arbitrary convex semi-algebraic sets,
present some recent results, and then apply them to the special case of
semidefinite programs to obtain the previously mentioned extension.

(Joint work with Leonid Khachiyan.)