An Approximate Solution to Unconstrained Multi-Objective Stochastic Optimization Problem
by
V. Charles
Department of Mathematics and Humanities, National Institute of Technology, Warangal, A.P., India
Coauthors: D. Dutta,Department of Mathematics and Humanities, National Institute of Technology, Warangal, A.P., India

This paper addresses an approximate solution to unconstrained multi-objective stochastic optimization problem (UMOSOP). UMOSOP is nothing but optimizing more than one objective function in which the underlying variables are random. A linear combination of stochastic objective functions has been obtained with the help of stochastic scalarizing function technique so as to get single objective function. It has been assumed that the probability laws of the random variables are unknown. Some estimates of the optimal solution and the optimal value of the optimized function were discussed in early literatures. These estimates were obtained using realizations of random variables having the same probability laws as those in the problem. We have investigated rate of convergence for these estimates. It has been shown that the convergence rate is at least exponential.

Date received: October 11, 2004