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Line Search and Merit Function
The solution to the QP subproblem produces a vector , which is used to form a new iterate
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(2-41) |
The step length parameter is determined in order to produce a sufficient decrease in a merit function. The merit function used by Han [22] and Powell [32] of the form below has been used in this implementation.
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(2-42) |
Powell recommends setting the penalty parameter
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(2-43) |
This allows positive contribution form constraints that are inactive in the QP solution but were recently active. In this implementation, initially the penalty parameter is set to
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(2-44) |
where represents the Euclidean norm.
This ensures larger contributions to the penalty parameter from constraints with smaller gradients, which would be the case for active constraints at the solution point.
![]() | Quadratic Programming Solution | Multiobjective Optimization | ![]() |