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- Renato D. C. Monteiro

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
38
Citations
8,353
128
World Ranking
1538
National Ranking
684

Engineering and Technology
D-index
38
Citations
8,350
129
World Ranking
4084
National Ranking
1371

- Mathematical analysis
- Algebra
- Geometry

His primary scientific interests are in Algorithm, Linear programming, Discrete mathematics, Semidefinite programming and Combinatorics. He is interested in Time complexity, which is a branch of Algorithm. His Linear programming study frequently draws connections between related disciplines such as Interior point method.

His Interior point method research is multidisciplinary, relying on both Logarithm, Numerical analysis and System of linear equations. The subject of his Semidefinite programming research is within the realm of Mathematical optimization. He interconnects Duality gap and Convex optimization in the investigation of issues within Combinatorics.

- A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization (651 citations)
- Interior path following primal-dual algorithms. Part I: Linear programming (380 citations)
- Primal--Dual Path-Following Algorithms for Semidefinite Programming (273 citations)

His primary areas of study are Interior point method, Mathematical optimization, Algorithm, Applied mathematics and Semidefinite programming. His study in Interior point method is interdisciplinary in nature, drawing from both Linear programming, Numerical analysis, Monotone polygon and System of linear equations. Renato D. C. Monteiro combines subjects such as Logarithm, Polynomial and Path following with his study of Linear programming.

His Mathematical optimization study integrates concerns from other disciplines, such as Newton's method and Convex analysis, Convex optimization. His Algorithm study combines topics in areas such as Duality gap, Quadratic programming, Feasible region and Order. Renato D. C. Monteiro has researched Semidefinite programming in several fields, including Second-order cone programming, Nonlinear programming, Combinatorics, Semidefinite embedding and Combinatorial optimization.

- Interior point method (38.28%)
- Mathematical optimization (30.47%)
- Algorithm (30.47%)

- Applied mathematics (28.12%)
- Regular polygon (13.28%)
- Sequence (10.16%)

His primary areas of investigation include Applied mathematics, Regular polygon, Sequence, Bounded function and Differentiable function. Renato D. C. Monteiro has included themes like Minification, Curvature, Gradient method, Composite optimization and Composite number in his Applied mathematics study. His studies deal with areas such as Logarithm and Type as well as Regular polygon.

His Type study frequently intersects with other fields, such as Combinatorics. In his research, Mathematical optimization is intimately related to Key, which falls under the overarching field of Proximal point method. Among his Non-Euclidean geometry studies, there is a synthesis of other scientific areas such as Discrete mathematics, Scale, Block and Algorithm.

- An accelerated non-Euclidean hybrid proximal extragradient-type algorithm for convex–concave saddle-point problems (27 citations)
- Complexity of a Quadratic Penalty Accelerated Inexact Proximal Point Method for Solving Linearly Constrained Nonconvex Composite Programs (24 citations)
- Improved Pointwise Iteration-Complexity of A Regularized ADMM and of a Regularized Non-Euclidean HPE Framework (19 citations)

- Mathematical analysis
- Algebra
- Geometry

The scientist’s investigation covers issues in Applied mathematics, Type, Non-Euclidean geometry, Regular polygon and Proximal point method. The Applied mathematics study combines topics in areas such as Constrained optimization problem, Bounded function, Composite optimization, Domain and Relaxation. His Bounded function research incorporates elements of Lagrange multiplier and Augmented Lagrangian method.

The concepts of his Type study are interwoven with issues in Saddle, Minification, Saddle point, Convex optimization and Algorithm. His Regular polygon research includes elements of Ergodic theory, Regularization and Logarithm. The study incorporates disciplines such as Structure, Quadratic equation, Composite number, Sequence and Stationary point in addition to Proximal point method.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization

Samuel Burer;Renato D.C. Monteiro.

Mathematical Programming **(2003)**

883 Citations

Interior path following primal-dual algorithms. Part I: Linear programming

Renato D.C. Monteiro;Ilan Adler.

Mathematical Programming **(1989)**

810 Citations

Primal--Dual Path-Following Algorithms for Semidefinite Programming

Renato D. C. Monteiro.

Siam Journal on Optimization **(1997)**

472 Citations

Local Minima and Convergence in Low-Rank Semidefinite Programming

Samuel Burer;Renato D. C. Monteiro.

Mathematical Programming **(2005)**

429 Citations

Interior path following primal-dual algorithms. Part II: Convex quadratic programming

Renato D.C. Monteiro;Ilan Adler.

Mathematical Programming **(1989)**

426 Citations

Dimension reduction and coefficient estimation in multivariate linear regression

Ming Yuan;Ali Ekici;Zhaosong Lu;Renato Monteiro.

Journal of The Royal Statistical Society Series B-statistical Methodology **(2007)**

340 Citations

A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension

R. C. Monteiro;I. Adler;M. G.C. Resende.

Mathematics of Operations Research **(1990)**

311 Citations

Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs

Samuel Burer;Renato D. C. Monteiro;Yin Zhang.

Siam Journal on Optimization **(2002)**

239 Citations

ITERATION-COMPLEXITY OF BLOCK-DECOMPOSITION ALGORITHMS AND THE ALTERNATING DIRECTION METHOD OF MULTIPLIERS ∗

Renato D. C. Monteiro;Benar Fux Svaiter.

Siam Journal on Optimization **(2013)**

227 Citations

Polynomial convergence of primal-dual algorithms for the second-order cone program based on the MZ-family of directions

Renato D.C. Monteiro;Takashi Tsuchiya.

Mathematical Programming **(2000)**

218 Citations

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