This work introduces a new analytical approach to the formulation of optimization problems with piecewise-defined (PD) objective functions. First, we introduce a new definition of multivariate PD functions and derive formal results for their continuity and differentiability. Then, we obtain closed-form expressions for the calculation of their moments. We apply these findings to three classes of optimization problems involving coherent risk measures. The method enables one to obtain insights on problem structure and on sensitivity to imprecision at the problem formulation stage, eliminating reliance on ad-hoc post-optimality numerical calculations. © 2008 Springer Science+Business Media, LLC.
Moment calculations for piecewise-defined functions: an application to stochastic optimization with coherent risk measures
BORGONOVO, EMANUELE;PECCATI, LORENZO
2010
Abstract
This work introduces a new analytical approach to the formulation of optimization problems with piecewise-defined (PD) objective functions. First, we introduce a new definition of multivariate PD functions and derive formal results for their continuity and differentiability. Then, we obtain closed-form expressions for the calculation of their moments. We apply these findings to three classes of optimization problems involving coherent risk measures. The method enables one to obtain insights on problem structure and on sensitivity to imprecision at the problem formulation stage, eliminating reliance on ad-hoc post-optimality numerical calculations. © 2008 Springer Science+Business Media, LLC.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.