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- R. Wets
- MathematicsAdvanced Optimization for Process Systems…
- 1 October 1989
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
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.
Minimization by Random Search Techniques
Two general convergence proofs for random search algorithms are given and how these extend those available for specific variants of the conceptual algorithm studied here are shown.
L-SHAPED LINEAR PROGRAMS WITH APPLICATIONS TO OPTIMAL CONTROL AND STOCHASTIC PROGRAMMING.
This paper gives an algorithm for L-shaped linear programs which arise naturally in optimal control problems with state constraints and stochastic linear programs (which can be represented in this…
Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse
Various approximation schemes for stochastic optimization problems involving either approximates of the probability measures and/or approximates of the objective functional, are investigated. We…
Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs
- D. Gade, Gabriel Hackebeil, S. Ryan, J. Watson, R. Wets, D. L. Woodruff
- Computer ScienceMath. Program.
- 1 May 2016
This work presents a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs, and explores the relationship between key PHA parameters and the quality of the resulting lower bounds.
ASYMPTOTIC BEHAVIOR OF STATISTICAL ESTIMATORS AND OF OPTIMAL SOLUTIONS OF STOCHASTIC OPTIMIZATION PROBLEMS
We study the asymptotic behavior of the statistical estimators that maximize a not necessarily dieren tiable criterion function, possibly subject to side constraints (equalities and inequalities).…
Nonanticipativity and L1-martingales in stochastic optimization problems
Necessary and sufficient conditions for optimality are derived for multistage stochastic programs. In particular it is shown that under some standard regularity conditions and a condition of…
Epi‐consistency of convex stochastic programs
This paper presents consistency results for sequences of optimal solutions to convex stochastic optimization problems constructed from empirical data, by applying the strong law of large numbers fo...