102 citations · 320 across the 34 of their papers we have counts for
27 papers · 1 filter
An efficient active-set method with applications to sparse approximations and risk minimization
Spyridon Pougkakiotis, Jacek Gondzio, Dionysis Kalogerias
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applica…
A regularized Interior Point Method for sparse Optimal Transport on Graphs
Stefano Cipolla, Jacek Gondzio, Filippo Zanetti
In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the in…
An active-set method for sparse approximations. Part II: General piecewise-linear terms
Spyridon Pougkakiotis, Jacek Gondzio, Dionysios S. Kalogerias
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applica…
Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming
Jacek Gondzio, Francisco N. C. Sobral
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system o…
An Interior-Point-Inspired algorithm for Linear Programs arising in Discrete Optimal Transport
Filippo Zanetti, Jacek Gondzio
Discrete Optimal Transport problems give rise to very large linear programs (LP) with a particular structure of the constraint matrix. In this paper we present a hybrid algorithm t…
Proximal stabilized Interior Point Methods for quadratic programming and low-frequency-updates preconditioning techniques
Stefano Cipolla, Jacek Gondzio
In this work, in the context of Linear and Quadratic Programming, we interpret Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Meth…
An active-set method for sparse approximations. Part I: Separable terms
Spyridon Pougkakiotis, Jacek Gondzio, Dionysios S. Kalogerias
In this paper we present an active-set method for the solution of -regularized convex quadratic optimization problems. It is derived by combining a proximal method of multi…
General-purpose preconditioning for regularized interior point methods
Jacek Gondzio, Spyridon Pougkakiotis, John W. Pearson
In this paper we present general-purpose preconditioners for regularized augmented systems arising from optimization problems, and their corresponding normal equations. We discuss…
A new stopping criterion for Krylov solvers applied in Interior Point Methods
Filippo Zanetti, Jacek Gondzio
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by desig…
Sparse Approximations with Interior Point Methods
Valentina De Simone, Daniela di Serafino, Jacek Gondzio +2
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods a…
Random multi-block ADMM: an ALM based view for the QP case
Stefano Cipolla, Jacek Gondzio
Embedding randomization procedures in the Alternating Direction Method of Multipliers (ADMM) has recently attracted an increasing amount of interest as a remedy to the fact that th…
An Interior Point-Proximal Method of Multipliers for Positive Semi-Definite Programming
Spyridon Pougkakiotis, Jacek Gondzio
In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programmi…
Fast Solution Methods for Convex Quadratic Optimization of Fractional Differential Equations
Spyridon Pougkakiotis, John W. Pearson, Santolo Leveque +1
In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on…
An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming
Spyridon Pougkakiotis, Jacek Gondzio
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual r…
Dynamic Non-Diagonal Regularization in Interior Point Methods for Linear and Convex Quadratic Programming
Spyridon Pougkakiotis, Jacek Gondzio
In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal e…
Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations
Jacek Gondzio, E. Alper Yildirim
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadrat…
Quasi-Newton approaches to Interior Point Methods for quadratic problems
J. Gondzio, F. N. C. Sobral
Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computation…
An inexact potential reduction method for linear programming
Lukas Schork, Jacek Gondzio
A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the sol…
Performance of First- and Second-Order Methods for L1-Regularized Least Squares Problems
Kimon Fountoulakis, Jacek Gondzio
We study the performance of first- and second-order optimization methods for l1-regularized sparse least-squares problems as the conditioning of the problem changes and the dimensi…
A Preconditioner for a Primal-Dual Newton Conjugate Gradients Method for Compressed Sensing Problems
Ioannis Dassios, Kimon Fountoulakis, Jacek Gondzio
In this paper we are concerned with the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. We extend…
Action constrained quasi-Newton methods
Robert Mansel Gower, Jacek Gondzio
At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separa…
A Second-Order Method for Compressed Sensing Problems with Coherent and Redundant Dictionaries
Ioannis Dassios, Kimon Fountoulakis, Jacek Gondzio
In this paper we are interested in the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. CS problems…
Large-scale optimization with the primal-dual column generation method
Jacek Gondzio, Pablo González-Brevis, Pedro Munari
The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted maste…
A Second-Order Method for Strongly Convex L1-Regularization Problems
Kimon Fountoulakis, Jacek Gondzio
In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as p…