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Robust Stochastic Approximation Approach to Stochastic Programming
- A. Nemirovski, A. Juditsky, Guanghui Lan, A. Shapiro
- Computer Science, MathematicsSIAM Journal on Optimization
- 1 December 2008
It is intended to demonstrate that a properly modified SA approach can be competitive and even significantly outperform the SAA method for a certain class of convex stochastic problems.
Lectures on Stochastic Programming - Modeling and Theory
- A. Shapiro, D. Dentcheva, A. Ruszczynski
- Materials ScienceMOS-SIAM Series on Optimization
- 24 September 2009
The authors dedicate this book to Julia, Benjamin, Daniel, Natan and Yael; to Tsonka, Konstatin and Marek; and to the Memory of Feliks, Maria, and Dentcho.
The Sample Average Approximation Method for Stochastic Discrete Optimization
A Monte Carlo simulation--based approach to stochastic discrete optimization problems, where a random sample is generated and the expected value function is approximated by the corresponding sample average function.
Perturbation Analysis of Optimization Problems
It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.
Convex Approximations of Chance Constrained Programs
A large deviation-type approximation, referred to as “Bernstein approximation,” of the chance constrained problem is built that is convex and efficiently solvable and extended to the case of ambiguous chance constrained problems, where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set.
Optimization of Convex Risk Functions
New representation theorems for risk models, and optimality and duality theory for problems with convex risk functions, are developed by employing techniques of convex analysis and optimization theory in vector spaces of measurable functions.
A stochastic programming approach for supply chain network design under uncertainty
Optimization Problems with Perturbations: A Guided Tour
The emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems allow one to compute expansions of the optimal value function and approximate optimal solutions in situations where the set of Lagrange multipliers is not a singleton, may be unbounded, or is even empty.
ON DUALITY THEORY OF CONIC LINEAR PROBLEMS
- A. Shapiro
In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We…