Patrick L. Combettes

What is he best known for?

The fields of study he is best known for:

• Mathematical analysis
• Statistics
• Algebra

His primary areas of study are Mathematical optimization, Convex optimization, Hilbert space, Algorithm and Monotone polygon. The various areas that he examines in his Mathematical optimization study include Convex function, Image restoration and Inverse problem. In the subject of general Convex optimization, his work in Convex analysis is often linked to Phase retrieval, thereby combining diverse domains of study.

His work carried out in the field of Hilbert space brings together such families of science as Range, Sparse approximation, Thresholding and Regular polygon. His research investigates the connection with Algorithm and areas like Convex set which intersect with concerns in Product topology and Parallel projection. His studies in Monotone polygon integrate themes in fields like Mathematical analysis, Resolvent, Combinatorics and Applied mathematics.

His most cited work include:

• Convex Analysis and Monotone Operator Theory in Hilbert Spaces (2553 citations)
• SIGNAL RECOVERY BY PROXIMAL FORWARD-BACKWARD SPLITTING ∗ (1865 citations)
• Proximal Splitting Methods in Signal Processing (1537 citations)

What are the main themes of his work throughout his whole career to date?

His primary scientific interests are in Mathematical optimization, Convex optimization, Monotone polygon, Algorithm and Hilbert space. His study in the field of Iterative method is also linked to topics like Signal processing. The concepts of his Convex optimization study are interwoven with issues in Linear matrix inequality and Inverse problem.

The Monotone polygon study combines topics in areas such as Fixed point, Pure mathematics, Duality, Applied mathematics and Monotonic function. His Algorithm research includes elements of Parallel projection, Orthonormal basis, Point and Iterative reconstruction. The concepts of his Hilbert space study are interwoven with issues in Range, Zero, Weak convergence and Composition.

He most often published in these fields:

• Mathematical optimization (40.82%)
• Convex optimization (28.98%)
• Monotone polygon (28.16%)

What were the highlights of his more recent work (between 2017-2021)?

• Monotone polygon (28.16%)
• Convex optimization (28.98%)
• Regular polygon (14.69%)

In recent papers he was focusing on the following fields of study:

His primary areas of investigation include Monotone polygon, Convex optimization, Regular polygon, Mathematical optimization and Nonlinear system. His Monotone polygon research is multidisciplinary, relying on both Operator splitting, Monotonic function, Pure mathematics and Minification. His work carried out in the field of Convex optimization brings together such families of science as Image recovery, Convex function, Linear combination and Statistical model.

His research in Convex function tackles topics such as Algorithm which are related to areas like Zero. The study of Mathematical optimization is intertwined with the study of Convex analysis in a number of ways. His Nonlinear system study incorporates themes from Fixed point, Affine transformation, Hilbert space and Variational inequality, Applied mathematics.

Between 2017 and 2021, his most popular works were:

• Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions (51 citations)
• Deep Neural Network Structures Solving Variational Inequalities (33 citations)
• Monotone operator theory in convex optimization (33 citations)

In his most recent research, the most cited papers focused on:

• Mathematical analysis
• Algebra
• Statistics

Patrick L. Combettes mainly focuses on Convex optimization, Mathematical optimization, Monotonic function, Algebra and Nonlinear system. His Convex optimization study combines topics in areas such as Fisher information and Addition theorem. Within one scientific family, Patrick L. Combettes focuses on topics pertaining to Regular polygon under Mathematical optimization, and may sometimes address concerns connected to Image recovery and Transformation.

His study explores the link between Monotonic function and topics such as Numerical analysis that cross with problems in Monotone polygon and Operator theory. His Nonlinear system research is multidisciplinary, incorporating perspectives in Fixed point and Applied mathematics. He interconnects Artificial neural network and Affine transformation in the investigation of issues within Applied mathematics.