Leung, YeeYeeLeungChen, Kai-ZhouKai-ZhouChenJiao, Yong-ChangYong-ChangJiaoGao, Xing-BaoXing-BaoGaoProf. LEUNG Kwong Sak2023-03-292023-03-292001IEEE Transactions on Neural Networks, 2001, Vol. 12 (5), pp. 1074 - 108310459227http://hdl.handle.net/20.500.11861/7654In this paper, a new gradient-based neural network is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory, and LaSalle invariance principle to solve linear and quadratic programming problems. In particular, a new function F(x, y) is introduced into the energy function E(x, y) such that the function E(x, y) is convex and differentiable, and the resulting network is more efficient. This network involves all the relevant necessary and sufficient optimality conditions for convex quadratic programming problems. For linear programming (LP) and quadratic programming (QP) problems with unique and infinite number of solutions, we have proven strictly that for any initial point, every trajectory of the neural network converges to an optimal solution of the QP and its dual problem. The proposed network is different from the existing networks which use the penalty method or Lagrange method, and the inequality (including nonnegativity) constraints are properly handled. The theory of the proposed network is rigorous and the performance is much better. The simulation results also show that the proposed neural network is feasible and efficient.enNeural NetworkLinear ProgrammingLinear ProblemQuadratic ProgrammingQuadratic Programming ProblemGradient-Based Neural NetworkEnergy FunctionInequality ConstraintsAsymptotically StablePenalty FunctionDual ProblemDual TheoryNon-Negativity ConstraintsLyapunov Stability TheoryConvex AnalysisSufficient Optimality ConditionsLaSalle’s Invariance PrincipleLagrange MultiplierEquilibrium PointEquality ConstraintsFeasible SetNeural Network OptimizationPrimal ProblemStability ProofConvex FunctionTransient BehaviorTheoretical SolutionNonlinear Programming ProblemDual SolutionPeer Reviewed Journal Article10.1109/72.950137