Sequential quadratic programming

Resources: page=550 ch 18

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Main Idea: Model the problem at the current iterate $x_k$ by a QP subproblem, then use the minimizer of this sub problem to define a new iterate $x_{k+1}$.

Builds on: Newton’s Method for Nonlinear Equations to solve Nonlinear Equations, in this case Exercise 4 - Quadratic Programming problems.

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Equality Constrained Problems

Generally on the form

$$\underset{x\in {\mathbb{R}}^n}{\min }f(x)s.t.c_i(x)=0,i\in \mathcal{E}$$

Where $c(x)=[c_1,c_2,\dots ,c_m]$, and $f$ is nonlinear