发表机构
Veermata Jijabai Technological Institute (VJTI); TenneT Offshore GmBH; IIT Chennai（维尔马塔·吉贾巴伊技术学院; TenneT Offshore GmBH; 金奈印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对约束优化问题，提出互流形退火KKT流框架，将其应用于IEEE节点系统的交流最优潮流，可保持约束可行性并降低计算复杂度。
AI 中文摘要
安全关键型优化应用（如实时电力系统运行）需在每一个中间步骤都保持可行性，而非仅在收敛时才满足。现有方法要么在求解过程中违反约束（内点法），要么通过瞬时二次量子问题强制执行可行性，其计算成本为立方级且最坏情况下执行时间无界。我们针对光滑约束非线性问题提出了一种连续时间优化框架，该框架在整个优化过程中保持可行性，无需投影算子、二次量子问题或其他逐次迭代优化例程。该方法基于互乘子流形构建，此流形建立了不等式约束与其关联拉格朗日乘子之间的显式关系。通过设计连续乘子更新律，可证明该流形保持前向不变性，且所得动力学等效于连续时间对数障碍梯度下降。所提框架自然扩展至多个不等式约束、等式约束、非凸可行集及不可行初始条件。该方法通过增广Uzawa流进一步增强，消除了经典原对偶鞍点动力学中常见的振荡瞬态。将所提方法应用于IEEE 9节点和IEEE 57节点系统的交流最优潮流问题，数值结果显示其收敛至与基准最优解偏差在0.4%以内的解，同时保持所有约束的严格可行性。计算复杂度分析表明，所提动力学将每步计算成本从立方级降低至线性级。最后，时变运行条件下的动态跟踪研究证明了其可靠的可行性保持能力。
英文摘要
Safety-critical optimization applications, such as real-time power system operation, maintain feasibility at every intermediate step, not merely at convergence. Existing approaches either violate constraints mid-solve (interior-point methods) or enforce feasibility through per-instant quadratic programming subproblems with cubic computational cost and unbounded worst-case execution time. We propose a continuous-time optimization framework for smooth constrained nonlinear problems that preserves feasibility throughout the optimization process without requiring projection operators, quadratic programming subproblems, or other per-iteration optimization routines. The method is built around a reciprocal multiplier manifold, which establishes an explicit relationship between inequality constraints and their associated Lagrange multipliers. By designing a continuous multiplier update law, the manifold is shown to remain forward invariant, while the resulting dynamics are equivalent to continuous-time logarithmic barrier gradient descent. The proposed framework naturally extends to multiple inequality constraints, equality constraints, nonconvex feasible sets, and infeasible initial conditions. The method is further enhanced through an augmented Uzawa flow that eliminates oscillatory transients commonly observed in classical primal-dual saddle-point dynamics. The effectiveness of the proposed approach is applied to the AC Optimal Power Flow problem of IEEE 9-bus and IEEE 57-bus systems. Numerical results show convergence to solutions within 0.4\% of the benchmark optimum while maintaining strict feasibility of all constraints. A computational complexity analysis shows that the proposed dynamics reduce the per-step computational cost from cubic to linear complexity. Finally, dynamic tracking studies under time-varying operating conditions demonstrate reliable feasibility preservation.
