Journal of Global Optimization
A new one-layer neural network for linear and quadratic programming
IEEE Transactions on Neural Networks
Fundamental matrix solutions of piecewise smooth differential systems
Mathematics and Computers in Simulation
A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side
Journal of Computational and Applied Mathematics
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Sliding modes are used to analyze a class of dynamical systems that solve convex programming problems. The analysis is carried out using concepts from the theory of differential equations with discontinuous right-hand sides and Lyapunov stability theory. It is shown that the equilibrium points of the system coincide with the minimizers of the convex programming problem, and that irrespective of the initial state of the system the state trajectory converges to the solution set of the problem. The dynamic behavior of the systems is illustrated by two numerical examples.