Optimization Toolbox

Line Search and Merit Function

The solution to the QP subproblem produces a vector , which is used to form a new iterate

(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.

(2-42)

Powell recommends setting the penalty parameter

(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

(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