We discuss a primal-dual algorithm for expontial-cone optimization. The algorithm is based on primal-dual scaling proposed by Tuncel, with similar properties as Nesterov-Todd scalings for symmetric cones. We also discuss a new corrector for nonsymmetric cones, which considerably reduces the number of iterations required to solve a number of test problems. This algorithm has recently been developed for version 9 of the MOSEK software.
joint work with Fatma Kilinc-Karzan
We consider the generalized trust region subproblem (GTRS) of minimizing a nonconvex quadratic objective over a nonconvex quadratic constraint. An obvious lifting of this problem recasts the GTRS as minimizing a linear objective subject to two nonconvex quadratic constraints. In this talk, we give an explicit characterization of the convex hull of this nonconvex region and show how it leads to a linear time (in the input size) algorithm for approximating the GTRS.
We discuss a generalization of Balas disjunctive cuts which introduces the concept of disjunctive conic cuts (DCCs) and disjunctive cylindrical cuts (DCyCs). The first part of this talk will summarize the main results about DCCs and DCyCs including some results about valid conic inequalities for hyperboloids and non-convex quadratic cones. In the second part, we will discuss some of the limitation of this approach to derive useful valid inequalities in the context of MISOCO. In the last part we explore the potential for implementation of DCCs and DCyC.