Neural Dynamics for Constrained Bi-Objective Quadratic Programming with Applications to Scientific Computing

Neural dynamics is a powerful tool to solve online optimization problems and has been used in many applications. However, some problems cannot be modelled as a single objective optimization and neural dynamics method does not apply. This paper proposes the first neural dynamics model to solve bi-objective constrained quadratic program, which opens the avenue to extend the power of neural dynamics to multi-objective optimization. We rigorously prove that the designed neural dynamics is globally convergent and it converges to the optimal solution of the bi-objective optimization in Pareto sense. Illustrative examples on bi-objective geometric optimization are used to verify the correctness of the proposed method. The developed model is also tested in scientific computing with data from real industrial data with demonstrated superior to rival schemes.