T R I C E
TRUST - REGION INTERIOR - POINT ALGORITHMS
FOR OPTIMAL CONTROL AND
ENGINEERING DESIGN PROBLEMS

TRICE is an optimization package being developed by J. E. Dennis, Jr. (Rice University), Matthias Heinkenschloss (Rice University, formerly Virginia Tech), and Luís N. Vicente (Universidade de Coimbra, formerly Rice University) for the solution of large nonlinear programming problems arising in optimal control and engineering design problems. Mathematically, the problems are of the form

 min f(y,u) , (P) s.t. c(y,u) = 0 , e(y,u) = 0 , h(y,u) <= 0 .
In (P) y denotes the states, u denotes the controls or design variables and c(y,u) = 0 represents the state equations (the governing equations). Additional constraints e(y,u) = 0 and h(y,u) <= 0 may be specified.

TRICE algorithms are designed to solve very large scale problems governed by partial differential equations. The algorithms utilize the particular structure of the problems, they allow the user to furnish efficient, application dependent linear system solvers, provide mechanisms to incorporate inexact solutions to linear systems and derivatives, and they are based on an object-oriented design. More information on this aspect of the TRICE package can be found in the TRICE design page.

TRICE algorithms use and extend techniques successfully applied to other optimization problems. The algorithms are based on sequential quadratic programming (SQP) methods, they use trust-region strategies to globalize the convergence and interior-point techniques to handle inequality constraints. See the TRICE algorithms page for more details.

TRICE algorithms have been applied to various optimal control and design problems. For a partial list see the TRICE applications.

The TRICE package is under development. Algorithms for the solution of special cases of the problem (P) have been devised and implemented. More information on the status of the TRICE project and on the availability of the TRICE package can be found in the TRICE software page.

TRICE homepage
Design Algorithms Applications Software

J.E. Dennis, Jr. Matthias Heinkenschloss Luís N. Vicente
Department of Computational and Applied Mathematics
Rice University
6100 S. Main Street
Houston, TX 77005
dennis@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University
6100 S. Main Street
Houston, TX 77005
heinken@caam.rice.edu
Departamento de Matemática