What Is Optimization Toolbox?

Constrained OptimizationInitialization. The algorithm requires a feasible point to start. If the currentpoint from the SQP method is not feasible, then you can find a point bysolving the linear programming problem(3-37)The notation indicates the ith row of the matrix A. You can find a feasiblepoint (if one exists) to Equation 3-37 by setting x to a value that satisfiesthe equality constraints. You can determine this value by solving an underoroverdetermined set of linear equations formed from the set of equalityconstraints. If there is a solution to this problem, then the slack variable isset to the maximum inequality constraint at this point.You can modify the preceding QP algorithm for LP problems by setting thesearch direction to the steepest descent direction at each iteration, whereis the gradient of the objective function (equal to the coefficients of the linearobjective function).(3-38)If a feasible point is found using the preceding LP method, the main QP phaseis entered. The search direction is initialized with a search directionfound from solving the set of linear equationswhere is the gradient of the objective function at the current iterate(i.e., ).(3-39)If a feasible solution is not found for the QP problem, the direction of searchfor the mainSQProutine is taken as one that minimizes .3-37