Two problems in convex conic optimization

Abstract

In the first part of the thesis we focus on smallest enclosing ball problem. We implement Nesterova??s smoothing technique and present a new modified back-tracking algorithm to solve the problem.The second part of the thesis is on the generalized convex quadratic semidefinite program (GQSDP). We use the primal-dual path following method to solve(GQSDP). To deal with the ill-conditioned linear system, we design two types of preconditioners and prove their effectiveness. At last, we show some numerical results on the primal-dual path following method of solving (QSDP).