{ max max f ¯ subject to: M { f ( x , ξ ) ≥ f ¯ } ≥ β M { g j ( x , ξ ) ≤ 0 } ≥ α j , j = 1 , 2 , ⋯ , p ( 2.10 ) where α j and β are specified confidence levels for j = 1 , 2 , ⋯ , p , and max f ¯ is the β -optimistic return. {\displaystyle {\begin{aligned}&\qquad \qquad \qquad {\begin{cases}\max \max {\bar {f}}\\{\text{subject to:}}\\\qquad {\mathcal {M}}\{f(x,\xi )\geq {\bar {f}}\}\geq \beta \\\qquad {\mathcal {M}}\{g_{j}(x,\xi )\leq 0\}\geq \alpha _{j},\quad j=1,2,\cdots ,p\end{cases}}\qquad \qquad (2.10)\\&{\text{where }}\alpha _{j}{\text{ and }}\beta {\text{ are specified confidence levels for }}j=1,2,\cdots ,p,{\text{ and }}\max {\bar {f}}\\&{\text{is the }}\beta {\text{-optimistic return.}}\end{aligned}}}