Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

Authors:
Naomi Miller;Andrzej Ruszczyński
Affiliations:
RUTCOR, Rutgers University, Piscataway, New Jersey 08854;Department of Management Science and Information Systems, Rutgers University, Piscataway, New Jersey 08854
Venue:
Operations Research
Year:
2011

Citing 8
Cited 0

A regularized decomposition method for minimizing a sum of polyhedral functions

Mathematical Programming: Series A and B
Dual Stochastic Dominance and Related Mean-Risk Models

SIAM Journal on Optimization
Risk Aversion via Excess Probabilities in Stochastic Programs with Mixed-Integer Recourse

SIAM Journal on Optimization
Convexity and decomposition of mean-risk stochastic programs

Mathematical Programming: Series A and B
Optimization of Convex Risk Functions

Mathematics of Operations Research
Conditional Risk Mappings

Mathematics of Operations Research
Nonlinear Optimization

Nonlinear Optimization
Risk-averse dynamic programming for Markov decision processes

Mathematical Programming: Series A and B - 20th International Symposium on Mathematical Programming – ISMP 2009

Quantified Score

Hi-index	0.00

Visualization

Abstract

We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct a new decomposition method for solving the problem that exploits the composite structure of the objective function. We illustrate its performance on a portfolio optimization problem.