Valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints

Stochastic dominance relations are well studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic optimization models involving second o...

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Vydáno v:Mathematical programming Ročník 114; číslo 2; s. 249 - 275
Hlavní autoři: Noyan, Nilay, Ruszczyński, Andrzej
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.08.2008
Springer
Springer Nature B.V
Témata:
Algorithms
Applied sciences
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Decision theory
Exact sciences and technology
Expected values
Flows in networks. Combinatorial problems
Full Length Paper
Linear programming
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Optimization
Portfolio theory
Probability
Random variables
Restrictions
Risk theory. Actuarial science
Stochastic models
Studies
Theoretical
Stochastic dominance
Valid inequalities
Disjunctive cuts
Stochastic programming
Conditional value at risk
Stochastic model
Combinatorial problem
Financial management
Combinatorial optimization
Modeling
Zero one programming
Economic theory
Disjunctive form
Discrete programming
Convexity
Mathematical programming
Statistical analysis
Probabilistic approach
Mixed programming
Linear programming
Risk analysis
Cut generation
Constrained optimization
Stochastic programming .Stochastic dominance .Valid inequalities .Disjunctive cuts .Conditional value at risk
Decision theory
Heuristic method
Risk management
Portfolio management
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí:Stochastic dominance relations are well studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic optimization models involving second order stochastic dominance constraints can be solved by linear programming. However, problems involving first order stochastic dominance constraints are potentially hard due to the non-convexity of the associated feasible regions. In this paper we consider a mixed 0–1 linear programming formulation of a discrete first order constrained optimization model and present a relaxation based on second order constraints. We derive some valid inequalities and restrictions by employing the probabilistic structure of the problem. We also generate cuts that are valid inequalities for the disjunctive relaxations arising from the underlying combinatorial structure of the problem by applying the lift-and-project procedure. We describe three heuristic algorithms to construct feasible solutions, based on conditional second order constraints, variable fixing, and conditional value at risk. Finally, we present numerical results for several instances of a real world portfolio optimization problem.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-007-0100-1