Finance Notes_Part_32

# Finance Notes_Part_32 - Open closed and hidden constraints...

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Open, closed and hidden constraints Consider the toy problem: min x R 2 x 2 1 - x 2 s.t. - x 2 1 + x 2 2 1 x 2 0 Closed constraints must be satisfied at every trial vector of decision variables in order for the functions to evaluate. Here x 2 0 is a closed constraint, because if it is violated, the objective function will fail. Open constraints must be satisfied at the solution, but an optimization algorithm may generate iterates that violate it. Here - x 2 1 + x 2 2 1 is an open constraint. Audet and Vicente (SIOPT 2008) Optimization under general constraints 80/109

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Open, closed and hidden constraints Consider the toy problem: min x R 2 x 2 1 - ln( x 2 ) s.t. - x 2 1 + x 2 2 1 x 2 0 Closed constraints must be satisfied at every trial vector of decision variables in order for the functions to evaluate. Here x 2 0 is a closed constraint, because if it is violated, the objective function will fail. Open constraints must be satisfied at the solution, but an optimization algorithm may generate iterates that violate it. Here
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