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Projected dynamical systems and optimization problems. (English) Zbl 1253.37091
Summary: We establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. A corresponding novel neural network model, which is globally convergent and stable in the sense of Lyapunov, is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for three constrained nonlinear optimization problems are given to show that the numerical behaviors are in good agreement with the theoretical results.

37N40 Dynamical systems in optimization and economics
90C30 Nonlinear programming
34K60 Qualitative investigation and simulation of models involving functional-differential equations
37M05 Simulation of dynamical systems