Sparse LP and QP Solvers

The previous chapter discussed methods for unconstrained optimization. For nonlinear constrained optimization problem, two powerful and commonly used algorithms are Sequential Linear Programming (SLP) and (SQP). Such algorithms solve a Linear Programming (LP) and Quadratic programming (QP) problems at each iteration. Therefore, the efficient implementation of NLP algorithms require efficient Linear Programming (LP) and Quadratic Programming (QP) solvers. In this chapter we discuss algorithms for LP and QP. The algorithms belong to a class of methods known as ‘active set’ methods which solve an equality constrained problem at each iteration where the equality constraints correspond to current guess of active constraints at the optimal. We begin with LP formulation.