Abstract: This report describes SDPpack Version 0.9 Beta for Matlab 5.0. This version extends the previous release for semidefinite programming (SDP) to mixed semidefinite--quadratic--linear programs (SQLP), i.e.\ linear optimization problems over a product of semidefinite cones, quadratic cones and the nonnegative orthant. Together, these cones make up all possible homogeneous self-dual cones over the reals.

The main routine implements a primal--dual Mehrotra predictor--corrector scheme based on the XZ+ZX search direction for SDP. More specialized routines are also available, one to solve SDP's with diagonal constraints only, and one to compute the Lov\'asz $\theta$ function of a graph, both using the XZ search direction. Routines are also provided to determine whether an SQLP is primal or dual degenerate at its solution and whether strict complementarity holds there. Primal nondegeneracy is associated with dual uniqueness and dual nondegeneracy with primal uniqueness, though these conditions are not equivalent if strict complementarity fails to hold.

A routine is also provided to compute the condition number of an SQLP. The Matlab code calls mex files for improved performance; binaries are available for several platforms. Benchmarks show that the codes provide highly accurate solutions to a wide variety of problems.