Optimization of conditional value-at risk
- R. Rockafellar, S. Uryasev
- Economics
- 2000
In an intensifying international competition banks are forced to place increased emphasis on enter-prise wide risk-/return management. Financial risks have to be limited and managed from a bank wide…
Monotone Operators and the Proximal Point Algorithm
- R. Rockafellar
- Mathematics
- 1 August 1976
For the problem of minimizing a lower semicontinuous proper convex function f on a Hilbert space, the proximal point algorithm in exact form generates a sequence $\{ z^k \} $ by taking $z^{k + 1} $…
Conditional Value-at-Risk for General Loss Distributions
- R. Rockafellar, S. Uryasev
- Economics
- 4 April 2001
Fundamental properties of conditional value-at-risk, as a measure of risk with significant advantages over value-at-risk, are derived for loss distributions in finance that can involve discreetness.…
Convex Analysis
- R. Rockafellar
- Computer SciencePrinceton Landmarks in Mathematics and Physics
- 1970
Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
- R. Rockafellar
- Computer Science, MathematicsMathematics of Operations Research
- 1 May 1976
The theory of the proximal point algorithm for maximal monotone operators is applied to three algorithms for solving convex programs, one of which has not previously been formulated and is shown to have much the same convergence properties, but with some potential advantages.
Variational Analysis
- R. Rockafellar, R. Wets
- Biology, ChemistryGrundlehren der mathematischen Wissenschaften
- 1998
Errata and Additions: December 2013 p.2-7 the x-axis should be just IR not IRn p.3-7 argmin f should be argminf̄ p.4-7 S(B) should be S (B) p.5-7 Proposition 4.
Scenarios and Policy Aggregation in Optimization Under Uncertainty
- R. Rockafellar, R. Wets
- Computer Science, EconomicsMathematics of Operations Research
- 1 February 1991
This paper develops for the first time a rigorous algorithmic procedure for determining a robust decision policy in response to any weighting of the scenarios.
Generalized deviations in risk analysis
- R. Rockafellar, S. Uryasev, M. Zabarankin
- MathematicsFinance and Stochastics
- 3 September 2004
Connections are shown with coherent risk measures in the sense of Artzner, Delbaen, Eber and Heath, when those are applied to the difference between a random variable and its expectation, instead of to the random variable itself.
Implicit Functions and Solution Mappings
- A. Dontchev, R. Rockafellar
- Mathematics
- 14 July 2009
The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. The…
Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming
- R. Rockafellar
- Mathematics, Economics
- 1 May 1974
If a nonlinear programming problem is analyzed in terms of its ordinary Lagrangian function, there is usually a duality gap, unless the objective and constraint functions are convex. It is shown he...
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