Projected Sequential Quadratic Programming Methods
Abstract
In this paper we introduce and analyze a class of optimization methods,
called projected sequential quadratic programming (SQP) methods,
for the solution of optimization problems
with nonlinear equality constraints and simple bound constraints on
parts of the variables. Such problems frequently arise in the numerical
solution of optimal control problems.
Projected SQP methods combine the ideas of projected Newton methods
and SQP methods.
They use the simple projection onto the set defined by
the bound constraints and maintain feasibility with respect to these
constraints.
The iterates are computed using an extension of SQP methods and only
require the solution of the linearized equality constraint.
Global convergence of these methods is enforced using a constrained merit
function and an Armijo-like line search.
We discuss global and local convergence properties of these methods, the
identification of active indices, and we present numerical examples
for an optimal control problem governed by a nonlinear heat
equation.
Keywords
Sequential quadratic programming methods, projected Newton methods,
merit function, bound constraints, optimal control
AMS subject classifications
49M37, 90C30