2013 - Khachiyan Prize of the INFORMS Optimization Society
2012 - SIAM Fellow For contributions to nonlinear, discrete, and convex optimization.
Donald Goldfarb mainly investigates Mathematical optimization, Algorithm, Convex optimization, Second-order cone programming and Quadratic programming. His biological study focuses on Semidefinite programming. The Algorithm study combines topics in areas such as Block and Special case.
His Convex optimization research includes themes of Robust principal component analysis, Numerical analysis, Missing data and Augmented Lagrangian method. His biological study spans a wide range of topics, including Quadratic equation and Interior point method. In his research on the topic of Matrix, Variable is strongly related with Applied mathematics.
The scientist’s investigation covers issues in Mathematical optimization, Algorithm, Applied mathematics, Linear programming and Combinatorics. Donald Goldfarb interconnects Second-order cone programming, Stationary point and Matrix completion in the investigation of issues within Mathematical optimization. Donald Goldfarb has included themes like Simplex, Matrix, Numerical analysis and Convex optimization in his Algorithm study.
The various areas that he examines in his Applied mathematics study include Hessian matrix, Gradient descent, Broyden–Fletcher–Goldfarb–Shanno algorithm, Quasi-Newton method and Rate of convergence. His Linear programming study combines topics in areas such as Ellipsoid method and Interior point method. His Combinatorics research integrates issues from Discrete mathematics and Upper and lower bounds.
His primary areas of investigation include Applied mathematics, Mathematical optimization, Broyden–Fletcher–Goldfarb–Shanno algorithm, Algorithm and Hessian matrix. He combines subjects such as Quasi-Newton method, Rate of convergence, Stochastic approximation and Stochastic optimization with his study of Applied mathematics. Donald Goldfarb has researched Mathematical optimization in several fields, including Gradient descent and Stationary point.
His Broyden–Fletcher–Goldfarb–Shanno algorithm study incorporates themes from Iterative method and Line. His work deals with themes such as Matrix and Unconstrained optimization, which intersect with Algorithm. His research investigates the connection between Hessian matrix and topics such as Curvature that intersect with problems in Function and Positive-definite matrix.
Applied mathematics, Stochastic optimization, Stochastic approximation, Variance reduction and Broyden–Fletcher–Goldfarb–Shanno algorithm are his primary areas of study. His work carried out in the field of Applied mathematics brings together such families of science as Rate of convergence, Curvature and Hessian matrix. His studies in Curvature integrate themes in fields like Positive-definite matrix, Gradient descent, Curvilinear coordinates, Function and Stationary point.
As part of one scientific family, Donald Goldfarb deals mainly with the area of Stochastic optimization, narrowing it down to issues related to the Almost surely, and often Mathematical optimization. The study incorporates disciplines such as Quasi-Newton method and Inverse in addition to Stochastic approximation. His Broyden–Fletcher–Goldfarb–Shanno algorithm study integrates concerns from other disciplines, such as Superlinear convergence, Iterative method, Line and Mathematical analysis.
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A family of variable-metric methods derived by variational means
Mathematics of Computation (1970)
An Iterative Regularization Method for Total Variation-Based Image Restoration
Stanley J. Osher;Martin Burger;Donald Goldfarb;Jinjun Xu.
Multiscale Modeling & Simulation (2005)
Second-order cone programming
Farid Alizadeh;Donald Goldfarb.
Mathematical Programming (2003)
Bregman Iterative Algorithms for $ll_1$-Minimization with Applications to Compressed Sensing
Wotao Yin;Stanley Osher;Donald Goldfarb;Jerome Darbon.
Siam Journal on Imaging Sciences (2008)
A numerically stable dual method for solving strictly convex quadratic programs
D. Goldfarb;A. Idnani.
Mathematical Programming (1983)
Fixed point and Bregman iterative methods for matrix rank minimization
Shiqian Ma;Donald Goldfarb;Lifeng Chen.
Mathematical Programming (2011)
Robust portfolio selection problems
D. Goldfarb;G. Iyengar.
Mathematics of Operations Research (2003)
The Ellipsoid Method: A Survey
Robert G. Bland;Donald Goldfarb;Michael J. Todd.
The Ellipsoid Method: A Survey (1980)
Alternating direction augmented Lagrangian methods for semidefinite programming
Zaiwen Wen;Donald Goldfarb;Wotao Yin.
Mathematical Programming Computation (2010)
Feature Article—The Ellipsoid Method: A Survey
Robert G. Bland;Donald Goldfarb;Michael J. Todd.
Operations Research (1981)
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