论文标题
耦合参数振荡器动力学与Lagrange乘法器原始双偶发优化的等效性
Equivalence of coupled parametric oscillator dynamics to Lagrange multiplier primal-dual optimization
论文作者
论文摘要
最近，人们对基于物理的求解器引起了共同优化问题的兴趣。我们为ISIN问题提供了一个动力求解器，该求解器由耦合参数振荡器网络组成，并表明它实现了Lagrange乘数约束优化。我们表明，与参数振荡器固有的泵耗尽效应强制执行二进制约束，并使系统的连续模拟变量能够收敛到优化问题的最佳二进制解决方案。此外，耦合振荡器的运动方程与Lagrange乘数的原始偶对偶数方法之间具有确切的对应关系。尽管我们的分析是使用电LC振荡器进行的，但可以将其推广到任何耦合参数振荡器系统。我们模拟了耦合振荡器系统的动力学，并证明求解器在一组基准问题上的性能与文献中数字算法获得的最著名结果相当。
There has been a recent surge of interest in physics-based solvers for combinatorial optimization problems. We present a dynamical solver for the Ising problem that is comprised of a network of coupled parametric oscillators and show that it implements Lagrange multiplier constrained optimization. We show that the pump depletion effect, which is intrinsic to parametric oscillators, enforces binary constraints and enables the system's continuous analog variables to converge to the optimal binary solutions to the optimization problem. Moreover, there is an exact correspondence between the equations of motion for the coupled oscillators and the update rules in the primal-dual method of Lagrange multipliers. Though our analysis is performed using electrical LC oscillators, it can be generalized to any system of coupled parametric oscillators. We simulate the dynamics of the coupled oscillator system and demonstrate that the performance of the solver on a set of benchmark problems is comparable to the best-known results obtained by digital algorithms in the literature.
