Orthogonal Projected Gradient Differential Neural Solution to Linear and Quadratic Constrained Optimization: Theory and Applications
提出一种正交投影梯度微分神经解法，用于解决线性和二次约束优化问题，理论证明其稳定性和收敛性，并在自适应波束成形和冗余机器人实验中验证了有效性。
In this research, an orthogonal projected gradient differential neural solution (OPGDNS) is introduced, specifically tailored for addressing linear and quadratic constrained optimization (LQCO) problems. The orthogonal projection theorem and gradient information are strategically leveraged, enabling the proposed solution to exhibit superior efficacy over existing methods, particularly those derived from a differential neural solution (DNS) standpoint, in handling linear and quadratic constraints. Theorems and proofs concerning the stability and convergence of the proposed OPGDNS model for LQCO problems are established. Finally, a numerical example is given, and experiments on the robust adaptive beamforming and the redundant robot are implemented, substantiating the applicability and advantage of the proposed OPGDNS model.