What is he best known for?
The fields of study he is best known for:
- Algebra
- Mathematical analysis
- Statistics
The scientist’s investigation covers issues in Mathematical optimization, Semidefinite programming, Convex optimization, Combinatorics and Discrete mathematics.
The various areas that Pablo A. Parrilo examines in his Mathematical optimization study include State and Linear dynamical system.
The concepts of his Semidefinite programming study are interwoven with issues in Quadratically constrained quadratic program, Real algebraic geometry, Polynomial, Combinatorial optimization and Sum-of-squares optimization.
His work carried out in the field of Convex optimization brings together such families of science as Floating point, Arbitrary-precision arithmetic, Algebra, Affine space and Applied mathematics.
His Combinatorics research is multidisciplinary, incorporating elements of Elementary symmetric polynomial, Symmetry, Convex hull and Symmetric polynomial.
His Discrete mathematics research incorporates themes from Multipartite entanglement, Quantum entanglement, Entanglement witness and Peres–Horodecki criterion.
His most cited work include:
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization (2790 citations)
- Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization (1666 citations)
- Constrained Consensus and Optimization in Multi-Agent Networks (1386 citations)
What are the main themes of his work throughout his whole career to date?
His scientific interests lie mostly in Combinatorics, Semidefinite programming, Mathematical optimization, Discrete mathematics and Polynomial.
Pablo A. Parrilo focuses mostly in the field of Combinatorics, narrowing it down to topics relating to Matrix and, in certain cases, Rank.
The Semidefinite programming study combines topics in areas such as Semidefinite embedding, Quadratically constrained quadratic program, Convex hull, Algebra and Upper and lower bounds.
His Mathematical optimization research incorporates elements of Algorithm, Lyapunov function and Convex optimization.
His studies in Convex optimization integrate themes in fields like Linear matrix inequality and Applied mathematics.
His study looks at the relationship between Polynomial and fields such as Explained sum of squares, as well as how they intersect with chemical problems.
He most often published in these fields:
- Combinatorics (30.33%)
- Semidefinite programming (28.67%)
- Mathematical optimization (24.67%)
What were the highlights of his more recent work (between 2014-2021)?
- Combinatorics (30.33%)
- Semidefinite programming (28.67%)
- Positive-definite matrix (8.33%)
In recent papers he was focusing on the following fields of study:
His primary areas of investigation include Combinatorics, Semidefinite programming, Positive-definite matrix, Discrete mathematics and Applied mathematics.
The study incorporates disciplines such as Matrix and Regular polygon in addition to Combinatorics.
His Semidefinite programming research is multidisciplinary, incorporating perspectives in Second-order cone programming, Rank, Algebra, Optimization problem and Upper and lower bounds.
As part of one scientific family, Pablo A. Parrilo deals mainly with the area of Optimization problem, narrowing it down to issues related to the Parsing, and often Algorithm.
His Discrete mathematics research integrates issues from Graph, Polynomial and Explained sum of squares.
Pablo A. Parrilo interconnects Stability, Exponential stability, Mathematical optimization, Hybrid system and Convex optimization in the investigation of issues within Lyapunov function.
Between 2014 and 2021, his most popular works were:
- On the Convergence Rate of Incremental Aggregated Gradient Algorithms (70 citations)
- Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-Offs (61 citations)
- Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone (56 citations)
In his most recent research, the most cited papers focused on:
- Algebra
- Mathematical analysis
- Statistics
His main research concerns Combinatorics, Semidefinite programming, Discrete mathematics, Positive-definite matrix and Convex function.
Pablo A. Parrilo studies Combinatorics, namely Chordal graph.
His research integrates issues of Fourier analysis, Optimization problem and Representation in his study of Semidefinite programming.
His Discrete mathematics study combines topics from a wide range of disciplines, such as Structure, Explained sum of squares, Algebraic number and Rank.
His research investigates the link between Structure and topics such as Interpretation that cross with problems in Applied mathematics.
His Rate of convergence research includes elements of Stochastic gradient descent, Mathematical optimization, Law of large numbers and Convex optimization.
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