Global optimization for non-convex programs via convex proximal point method

Proximal Point Nonlinear Rescaling Method for Convex Optimization

Nonlinear rescaling (NR) methods alternate finding an unconstrained minimizer of the Lagrangian for the equivalent problem in the primal space (which is an infinite procedure) with Lagrange multipliers update. We introduce and study a proximal point nonlinear rescaling (PPNR) method that preserves convergence and retains a linear convergence rate of the original NR method and at the same time d...

Interior-point method for non-linear non-convex optimization

Convex Optimization For Non-Convex Problems via Column Generation

We apply column generation to approximating complex structured objects via a set of primitive structured objects under either the cross entropy or L2 loss. We use L1 regularization to encourage the use of few structured primitive objects. We attack approximation using convex optimization over an infinite number of variables each corresponding to a primitive structured object that are generated ...

Global convergence of an inexact interior-point method for convex quadratic‎ ‎symmetric cone programming‎

‎In this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎The proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the Newton equation system‎, ‎by using an inexact Newton direction‎. ‎Furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

Augmented Lagrangian Methods and Proximal Point Methods for Convex Optimization

We present a review of the classical proximal point method for nding zeroes of maximal monotone operators, and its application to augmented Lagrangian methods, including a rather complete convergence analysis. Next we discuss the generalized proximal point methods, either with Bregman distances or -divergences, which in turn give raise to a family of generalized augmented Lagrangians, as smooth...