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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: [email protected] 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).