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- Farid Alizadeh, Donald Goldfarb
- Math. Program.
- 2003

the date of receipt and acceptance should be inserted later

- Shiqian Ma, Donald Goldfarb, Lifeng Chen
- Math. Program.
- 2011

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear norm minimization. Although the latter can be cast as a semidefinite programming problem, such an approach is… (More)

- Stanley Osher, Martin Burger, Donald Goldfarb, Jinjun Xu, Wotao Yin
- Multiscale Modeling & Simulation
- 2005

We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods, by using total variation regularization. We obtain rigorous convergence results, and… (More)

- Donald Goldfarb, Garud Iyengar
- Math. Oper. Res.
- 2003

In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce " uncertainty structures " for the market parameters and show… (More)

- Donald Goldfarb, Ashok U. Idnani
- Math. Program.
- 1983

An efficient and numerically stable dual algorithm for positive definite quadratic programming is described which takes advantage of the fact lhat the unconstrained minimum of the objective function can be used as a starling point. Its implementation utilizes the Cholesky and QR factorizations and procedures for updating them. The performance of the dual… (More)

- Lifeng Chen, Donald Goldfarb
- Math. Program.
- 2006

We propose two line search primal-dual interior-point methods that have a generic barrier-SQP outer structure and approximately solve a sequence of equality constrained barrier sub-problems. To enforce convergence for each subproblem, these methods use an ℓ 2-exact penalty function eliminating the need to drive the corresponding penalty parameter to… (More)

- Wotao Yin, Stanley Osher, Donald Goldfarb, Jérôme Darbon
- SIAM J. Imaging Sciences
- 2008

We propose simple and extremely efficient methods for solving the basis pursuit problem min{{u1 : Au = f, u ∈ R n }, which is used in compressed sensing. Our methods are based on Bregman iterative regularization, and they give a very accurate solution after solving only a very small number of instances of the unconstrained problem min u∈R n μu1 + 1 2 Au − f… (More)

- Donald Goldfarb, Shiqian Ma
- Foundations of Computational Mathematics
- 2011

The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization problem, is often solved instead. Recently, Ma, Goldfarb and Chen proposed a fixed-point continuation algorithm for… (More)

- Zaiwen Wen, Donald Goldfarb, Wotao Yin
- Math. Program. Comput.
- 2010

We present an alternating direction method based on an augmented Lagrangian framework for solving semidef-inite programming (SDP) problems in standard form. At each iteration, the algorithm, also known as a two-splitting scheme, minimizes the dual augmented Lagrangian function sequentially with respect to the Lagrange multipliers corresponding to the linear… (More)

- Donald Goldfarb
- Math. Program.
- 1980

The Armijo and Goldstein step-size rules are modified to allow steps along a curvilinear path of the form x(a) = x + as + a2d, where x is the current estimate of the minimum, s is a descent direction and d is a nonascent direction of negative curvature. By using directions of negative curvature when they exist, we are able to prove, under fairly mild… (More)