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Ralph Tyrrell Rockafellar (born February 10, 1935) is an American mathematician and one of the leading scholars in optimization theory and related fields of analysis and combinatorics. He is the author of four major books including the landmark text "Convex Analysis" (1970), [ 1 ] which has been cited more than 27,000 times according to Google ...
Roger Jean-Baptiste Robert Wets (born February 1937) is a "pioneer" in stochastic programming [2] and a leader in variational analysis who publishes as Roger J-B Wets.His research, expositions, graduate students, and his collaboration with R. Tyrrell Rockafellar have had a profound influence on optimization theory, computations, and applications.
Fenchel's duality theorem. In mathematics, Fenchel's duality theorem is a result in the theory of convex functions named after Werner Fenchel. Let ƒ be a proper convex function on Rn and let g be a proper concave function on Rn. Then, if regularity conditions are satisfied,
Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective, but the augmented Lagrangian method adds yet another term designed to mimic a Lagrange multiplier.
Variational analysis. In mathematics, variational analysis is the combination and extension of methods from convex optimization and the classical calculus of variations to a more general theory. [1] This includes the more general problems of optimization theory, including topics in set-valued analysis, e.g. generalized derivatives .
bPOE has its origins in the concept of buffered probability of failure (bPOF), developed by R. Tyrrell Rockafellar and Johannes Royset to measure failure risk. It was further developed and defined as the inverse CVaR by Matthew Norton, Stan Uryasev, and Alexander Mafusalov.
The subdifferential on convex functions was introduced by Jean Jacques Moreau and R. Tyrrell Rockafellar in the early 1960s. The generalized subdifferential for nonconvex functions was introduced by F.H. Clarke and R.T. Rockafellar in the early 1980s. [4]
The main article for this category is Variational analysis. Following the book Variational Analysis by Rockafellar and Wets, the term " variational analysis " denotes an extension of the classic calculus of variations and convex analysis to more general problems of optimization theory, including topics in set-valued analysis, e.g. generalized ...