Stochastic optimization using a non - derivative - trust region approach with variance reduction / Azza Adel Ahmed Rabie ; Supervised Hany Abd El Malek , Abd El Karim Shabaan Hassan

Thesis (Ph.D.) - Cairo University - Faculty Of Engineering - Department Of Mathematics and Physics

In this thesis , a new methodology has been proposed to solve stochastic optimization problems whose objective functions can be formulated as an expectation of an acceptance indexSuch problems arise in many important engineering applications whose decision variables have a random natureThis randomness is due to measurement errors or uncontrollable factors that affect the variablesAnother source of randomness appears when the considered problem involves some hardly computable mathematical formula such as multidimensional integralsIn these cases , the only way to evaluate the objective function is by statistical estimation , in which obtaining precise values is computationally expensive and time consumingTypically , for such stochastic problems , the derivative information is unavailable and unreliable to be approximated with the finite difference approachThe presence of the mentioned difficulties represents a great challenge to mathematicians since the traditional derivative - based optimization methods always break down in these circumstances

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