Solving quantile-based stochastic optimization problems with modified Stochastic Nelder-Mead Simplex Method

Quantile is one of the major metrics used in risk management. Since qauantile represents the downside risk. In this paper, we present a new variant of Nelder-Mead method (NM) for quantile-based stochastic optimization, called Stochastic Nelder-Mead Simplex Method for Quantile (SNM-Q), that aims to minimize the downside of decisions made in stochastic environments. An extensive numerical study shows that SNM-Q can efficiently and effectively control the risk and thus is worth further investigation.