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Optimization of conditional value-at risk
A new approach to optimizing or hedging a portfolio of nancial instruments to reduce risk is presented and tested on applications. It focuses on minimizing Conditional Value-at-Risk (CVaR) ratherExpand
Convex Analysis
  • R. Rockafellar
  • Computer Science
  • Princeton Landmarks in Mathematics and Physics
  • 1970
Monotone Operators and the Proximal Point Algorithm
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} $Expand
Conditional Value-at-Risk for General Loss Distributions
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.Expand
Variational Analysis
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. Expand
Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
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. Expand
Scenarios and Policy Aggregation in Optimization Under Uncertainty
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. Expand
Conditional Value-at-Risk for General Loss Distributions
Fundamental properties of conditional value-at-risk are derived for loss distributions in finance that can involve discreetness and provides optimization shortcuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach. Expand
Conjugate Duality and Optimization
The Role of Convexity and Duality Examples of Convex Optimization Problems Conjugate Convex Functions in Paired Spaces Dual Problems and Lagrangians Examples of Duality Schemes Continuity andExpand
On the maximality of sums of nonlinear monotone operators
is called the effective domain of F, and F is said to be locally bounded at a point x e D(T) if there exists a neighborhood U of x such that the set (1.4) T(U) = (J{T(u)\ueU} is a bounded subset ofExpand