Cutting plane algorithms for robust conic convex optimization

In the paper we study some well-known cases of nonlinear programming problems, presenting them as instances of Inexact Linear Programming. The class of problems considered contains, in particular, semidefinite programming, second order cone programming and special cases of inexact semidefinite programming. Strong duality results for the nonlinear problems studied are obtained via the Lagrangian duality. Using these results we propose some dual algorithms for the studied classes of problems. The proposed algorithms can be interpreted as cutting plane or discretization algorithms. Finally some comments on the convergence of the proposed algorithms and on some preliminary numerical tests are given.


Optimization Methods & Software, Vol. 21, Nr. 5, 2006