TRICE algorithms use and extend techniques
successfully applied in other optimization contexts.
- The TRICE algorithms
are based on sequential quadratic
programming (SQP) methods.
They compute a solution to the nonlinear programming problem by
solving a sequence of quadratic
programming problems.
States and controls are treated as independent variables.
The nonlinear constraints are not solved in every iteration;
the iterates approach feasibility and optimality
at the same time.
- Trust-region methods are used to guarantee
convergence from any starting point and
to introduce an implicit
regularization of the subproblems.
- Interior-point techniques
are used to handle inequality constraints.
- Provision is made not only to allow the inexact solution
of the QP subproblems, but, more importantly, to
allow for inexact solutions of linear systems
and inexact derivative information provided by
the user.
The TRICE algorithms and their convergence
properties are described in several
papers
and in the manuals contained in the
TRICE software page .