Polynomial Primal Dual Cone Affine Scaling for Semidefinite Programming

Semide nite programming concerns the problem of optimizing a linear function over a section of the cone of semide nite matrices In the cone a ne scaling approach we replace the cone of semide nite matrices by a certain inscribed cone in such a way that the resulting optimization problem is analytically solvable The now easily obtained solution to this modi ed problem serves as an approximate solution to the semide nite programming problem The inscribed cones that we use are a ne transformations of second order cones hence the name cone a ne scaling Compared to other primal dual a ne scaling algorithms for semide nite programming see De Klerk Roos and Terlaky our algorithm enjoys the lowest computational complexity AMS subject classi cation C C