Spyridon Pougkakiotis – Optimization Online

Sparse Approximations with Interior Point Methods

Published: 2021/03/01, Updated: 2021/11/25

Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization classification in machine learning, image reconstruction, interior point methods, nonlinear convex programming, portfolio optimization, proximal methods of multipliers, solution of kkt systems, sparse approximations

Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience … Read more

A New Preconditioning Approach for an Interior Point-Proximal Method of Multipliers for Linear and Convex Quadratic Programming

Published: 2019/12/20

Spyridon Pougkakiotis

Convex Optimization, Linear Programming, Quadratic Programming interior point methods, krylov methods, preconditioners, primal-dual regularization, proximal point algorithm

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers, which in turn results in a primal-dual regularized interior point method. Application of this method gives rise to a … Read more