EXTENSION OF KARMARKAR ALGORITHM ONTO CONVEX QUADRATICALLY CONSTRAINED QUADRATIC PROBLEMS

Convex quadratically constrained quadratic problems are considered. It is shown that such problems can be transformed to a conic form. The f easible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with a hyperplane (the analogu e of a simplex), and a linear subspace. For a problem of such form, th e analogue of Karmarkar's projective transformation and logarithmic ba rrier function are built. This allows us to extend ''word by word'' th e method of Karmarkar for LP to QCQP and allows us to obtain a similar polynomial worst-case bound for the number of iterations.