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- Benjamin Recht, Maryam Fazel, Pablo A. Parrilo
- SIAM Review
- 2010

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved… (More)

- Pablo A. Parrilo
- 2000

In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI) whose optimal solution can be characterized exactly. This family corresponds to the case where the associated linear operator maps the cone of positive semidefinite matrices onto itself. In this case, the optimal value equals the spectral radius of the… (More)

- Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo, Alan S. Willsky
- Foundations of Computational Mathematics
- 2012

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of… (More)

- Pablo A. Parrilo
- Math. Program.
- 2003

A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility. The main tools employed are a semidefinite programming formulation… (More)

- Venkat Chandrasekaran, Sujay Sanghavi, Pablo A. Parrilo, Alan S. Willsky
- SIAM Journal on Optimization
- 2011

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is NP-hard in general. In this paper we consider a convex optimization… (More)

- Angelia Nedic, Asuman E. Ozdaglar, Pablo A. Parrilo
- IEEE Trans. Automat. Contr.
- 2010

We present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time-varying connectivity. Our framework is general in that this value can represent a consensus value among multiple agents or an optimal solution of an optimization problem, where the global objective function is a… (More)

- Ali Jadbabaie, John Doyle, +5 authors Luz Vela
- 2000

With the advent of faster and cheaper computers, optimization based control methodologies have become a viable candidate for control of nonlinear systems. Over the past twenty years, a group of such control schemes have been successfully used in the process control industry where the processes are either intrinsically stable or have very large time… (More)

SOSTOOLS is a MATLAB toolbox for constructing and solving sum of squares programs. It can be used in combination with semidefinite programming software, such as SeDuMi, to solve many continuous and combinatorial optimization problems, as well as various control-related problems. This paper provides an overview on sum of squares programming, describes the… (More)

- Venkat Chandrasekaran, Pablo A. Parrilo, Alan S. Willsky
- 2010 48th Annual Allerton Conference on…
- 2010

Suppose we have samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to discover the number of hidden components, and to learn a statistical model over the entire collection of variables? We… (More)

- Pablo A. Parrilo, Bernd Sturmfels
- Algorithmic and Quantitative Aspects of Real…
- 2001

We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gröbner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation technique, due to N.Z. Shor and the first author, which involves sums of squares and semidefinite programming. This opens up… (More)