Int. Conference on Boundary and Interior Layers
BAIL 2006
G.Lube, G.Rapin (Eds)
 University of Göttingen, 2006
BAIL 2002 Sample Paper: A Unified Gradient Flow Approach to
Constrained Nonlinear Optimization Problems
S. Wang
Department of Mathematics and Statistics
University of Western Australia
35 Stirling Hwy, Crawley 6009, Australia
e-mail: swang@maths.uwa.edu.au
1. Introduction
Constrained nonlinear programming problems appear in almost every subject in engineering,
science, economics, finance and management. Many efficient methods have been developed for
solving problems with nonlinear inequality constraints. However, most of these methods fail to be
effective when they are applied to problems with equality constraints without the use of other
techniques such as penalty function approaches. Recently, gradient flow type methods have been
successfully used for solving this kind of problems by various authors (cf., for example, [1, 2]). In this
approach an optimization problem is formulated as an ordinary differential equation (ODE) so that the
solution of this ODE converges to a local minimum of the original problem as t → ∞.
2. Problems with equality constraints
More text….
References
[1] Y.G. Evtushenko and V.G. Zhadan, “Stable barrier-projection and barrier Newton methods in
nonlinear programming”, Optimization Methods and Software, 3, 237–256 (1994).
[2] Y.G. Evtushenko and V.G. Zhadan, “Stable barrier-projection and barrier Newton methods in
linear programming”, Computational Optimization and Applications, 3, 289–303 (1994).