000196203 001__ 196203
000196203 005__ 20190316235833.0
000196203 0247_ $$2doi$$a10.1007/s10107-009-0331-4
000196203 022__ $$a1436-4646
000196203 037__ $$aARTICLE
000196203 245__ $$aPrimal and dual linear decision rules in stochastic and robust optimization
000196203 260__ $$c2011
000196203 269__ $$a2011
000196203 336__ $$aJournal Articles
000196203 520__ $$aLinear stochastic programming provides a flexible toolbox for analyzing real-life decision situations, but it can become computationally cumbersome when recourse decisions are involved. The latter are usually modeled as decision rules, i.e., functions of the uncertain problem data. It has recently been argued that stochastic programs can quite generally be made tractable by restricting the space of decision rules to those that exhibit a linear data dependence. In this paper, we propose an efficient method to estimate the approximation error introduced by this rather drastic means of complexity reduction: we apply the linear decision rule restriction not only to the primal but also to a dual version of the stochastic program. By employing techniques that are commonly used in modern robust optimization, we show that both arising approximate problems are equivalent to tractable linear or semidefinite programs of moderate sizes. The gap between their optimal values estimates the loss of optimality incurred by the linear decision rule approximation. Our method remains applicable if the stochastic program has random recourse and multiple decision stages. It also extends to cases involving ambiguous probability distributions.
000196203 6531_ $$aLinear decision rules
000196203 6531_ $$aStochastic optimization
000196203 6531_ $$aRobust optimization
000196203 6531_ $$aError bounds
000196203 6531_ $$aSemidefinite programming
000196203 6531_ $$a90C15 (Stochastic Programming)
000196203 700__ $$0247589$$g239987$$aKuhn, Daniel
000196203 700__ $$aWiesemann, Wolfram
000196203 700__ $$aGeorghiou, Angelos
000196203 773__ $$j130$$tMathematical Programming$$k1$$q177-209
000196203 8564_ $$uhttp://link.springer.com/article/10.1007%2Fs10107-009-0331-4$$zURL
000196203 909C0 $$xU12788$$0252496$$pRAO
000196203 909CO $$ooai:infoscience.tind.io:196203$$qGLOBAL_SET$$pCDM$$particle
000196203 917Z8 $$x112541
000196203 937__ $$aEPFL-ARTICLE-196203
000196203 973__ $$rNON-REVIEWED$$sPUBLISHED$$aEPFL
000196203 980__ $$aARTICLE