Cutting plane algorithms for robust conic convex optimization problems

In this paper, we study some well-known cases of nonlinear programming problems, presenting them as instances of inexact or semi-infinite linear programming. The class of problems considered contains, in particular, semi-definite programming, second-order cone programming and special cases of inexact semi-definite 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 preliminary numerical tests are given.