Abstract
Conditional value at risk (CVaR) is often used to measure and manage risks in financial engineering. In this paper, we consider optimization problems with CVaR constraints. Due to the profound randomness and complexities, the CVaR constraints can only be estimated by stochastic simulation. We propose a new algorithm, called adaptive pattern search (APS) based on the pattern search method in the literature but further incorporates efficient modifications, including the determination of the moving directions, to enable the problem to be solved efficiently. Moreover, we applied Latin hypercube sampling (LHS) to determine a set of solutions for the algorithm to get started for better search of the optimal solution. A numerical study shows that the proposed algorithm is efficient and is worthy of further investigation.