In this paper, we analyze the numerical behaviour of a separable Augmented Lagrangian algorithm with multiple scaling parameters, different parameters associated with each dualized coupling constraint as well as with each subproblem. We show that an optimal superlinear rate of convergence can be theoretically attained in the twice differentiable case and propose an adaptive scaling … Read more
Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to … Read more
This paper studies an alternative technique to interior point methods and nonlinear methods for semidefinite programming (SDP). The approach based on classical quadratic regularizations leads to an algorithm, generalizing a recent method called “boundary point method”. We study the theoretical properties of this algorithm and we show that in practice it behaves very well on … Read more
We analyze the properties of an interior point cutting plane algorithm that is based on a semi-infinite linear formulation of the dual semidefinite program. The cutting plane algorithm approximately solves a linear relaxation of the dual semidefinite program in every iteration and relies on a separation oracle that returns linear cutting planes. We show that … Read more
We consider the problem of computing the smallest contact forces, with point-contact friction model, that can hold an object in equilibrium against a known external applied force and torque. It is known that the force optimization problem (FOP) can be formulated as a semidefinite programming problem (SDP), or a second-order cone problem (SOCP), and so … Read more
We describe a specialized truncated-Newton primal-dual interior-point method that solves large scale network utility maximization problems, with concave utility functions, efficiently and reliably. Our method is not decentralized, but easily scales to problems with a million flows and links. We compare our method to a standard decentralized algorithm based on dual decomposition, and show by … Read more
We describe graph implementations, a generic method for representing a convex function via its epigraph, described in a disciplined convex programming framework. This simple and natural idea allows a very wide variety of smooth and nonsmooth convex programs to be easily specified and efficiently solved, using interior-point methods for smooth or cone convex programs. CitationTo … Read more
The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation. The proposed l_1 trend filtering method substitutes a sum of absolute values (i.e., l_1-norm) for the sum of squares used in … Read more
In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of this paper is to compare two computational approaches based on Monte … Read more
In this paper we analyze several new methods for solving optimization problems with the objective function formed as a sum of two convex terms: one is smooth and given by a black-box oracle, and another is general but simple and its structure is known. Despite to the bad properties of the sum, such problems, both … Read more