What Is Optimization Toolbox?

Constrained Optimizationis updated at each iteration k, and this is used to form a basis for a searchdirection . Equality constraints always remain in the active set .Thenotation for the variable is used here to distinguish it from in the majoriterations of the SQP method. The search direction is calculated andminimizes the objective function while remaining on any active constraintboundaries. The feasible subspace for is formed from a basis whosecolumns are orthogonal to the estimate of the active set (i.e., ).Thus a search direction, which is formed from a linear summation of anycombination of the columns of , is guaranteed to remain on the boundariesof the active constraints.The matrix is formed from the last columns of the QR decompositionof the matrix ,wherel is the number of active constraints and l