R. Monteiro

Publications125
h-index35
Citations5,279
Highly Influential Citations566
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
TLDR
A nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form that replaces the symmetric, positive semideFinite variable X with a rectangular variable R according to the factorization X=RRT.
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Primal-Dual Path-Following Algorithms for Semidefinite Programming
TLDR
Two search directions within their family are characterized as being (unique) solutions of systems of linear equations in symmetric variables and, for the first time, a polynomially convergent long-step path-following algorithm for SDP which requires an extra $\sqrt{n}$ factor in its iteration-complexity order as compared to its linear programming counterpart.
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Local Minima and Convergence in Low-Rank Semidefinite Programming
TLDR
The local minima of LRSDPr are classified and the optimal convergence of a slight variant of the successful, yet experimental, algorithm of Burer and Monteiro is proved, which handles L RSDPr via the nonconvex change of variables X=RRT.
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Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs
The Goemans--Williamson randomized algorithm guarantees a high-quality approximation to the MAX-CUT problem, but the cost associated with such an approximation can be excessively high for large-scale…
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An Accelerated Hybrid Proximal Extragradient Method for Convex Optimization and Its Implications to Second-Order Methods
TLDR
This paper presents an accelerated variant of the hybrid proximal extragradient (H PE) method for convex optimization, referred to as the accelerated HPE (A-HPE) framework, as well as a special version of it, where a large stepsize condition is imposed.
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Dimension reduction and coefficient estimation in multivariate linear regression
Summary  We introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. We argue that many of the existing methods that are commonly used in…
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On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean
TLDR
This paper analyzes the iteration complexity of the hybrid proximal extragradient (HPE) method for finding a zero of a maximal monotone operator recently proposed by Solodov and Svaiter and obtains new complexity bounds for Korpelevich's extrag Radient method which do not require the feasible set to be bounded.
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A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite programming
TLDR
It is shown that within the class of algorithms studied in this paper, the one based on the Nesterov—Todd direction has the lowest possible iteration-complexity bound that can provably be derived from the analysis.
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Polynomial convergence of primal-dual algorithms for the second-order cone program based on the MZ-family of directions
TLDR
The polynomial convergence of primal-dual algorithms for SOCP based on a family of directions that is a natural extension of the Monteiro-Zhang (MZ) family for semidefinite programming is established for the first time.
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A projected gradient algorithm for solving the maxcut SDP relaxation
TLDR
A projected gradient algorithm for solving the semidefinite programming (SDP) relaxation of the maximum cut (maxcut) problem is presented and combined with a randomized method this gives a very efficient approximation algorithm for the maxcut problem.
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