Sequential linear quadratic programming

One of its important applications is as the first phase in identifying which constraints are active and passive. For example, it is adopted in the SLQP method (Sequential Linear Quadratic Programming) (see Nocedal and Wright, 2000). 

Problem Type Dense linear and nonlinear programs Method Sequential quadratic programming... 

Lagrange multiphers for, 2553-2554 and nonsmooth optimization, 2562 quadratic programming problems, 2555, 2562 separable programming problems, 2556-2558 sequential unconstrained minimization techniques for, 2560-2562 successive linear programming, 2562 successive quadratic programming, 2562 Constraint(s) ... 

The Lagrange function is approximated with a quadratic function, whereas the nonlinear constraints are linearized (Sequential Quadratic Programming, SQP, method see Section 13.7). Also in this case, a lower level BzzConstrai-nedMinimization class object with a quadratic objective function and hnear constraints is invoked. 

The problem of minimum as formulated above can be solved by sequential methods of nonlinear (in particular quadratic) programming. The idea of the sequential approach consists, most simply, in linearizing the equation g(z) = 0 at point z of the sequence and subjecting the linearized constraint equation to a minimum condition thus the next approximation is found, and so on. Some problems can arise when the whole unmeasured vector y is not observable (not uniquely determined) although the latter case is less frequent in practice, possibly it can happen that the values of some unmeasured variables are not required and admitted as unobservable (undetermined). In what follows we shall outline two methods that do not require the full observability of vector y. 

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