Primal–dual quasi-Newton (PDQN)PDQN-APPCoordinated corrective control (CC) is indispensable for protecting multi-area interconnected power grids operated by independent entities against post-contingency overloads, and even subsequent cascading failures. Generally, CC strategies are generated online by ...
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or
Qi, L., Jiang, H.: Semismooth Karush-Kuhn-Tucker equations and convergence analysis of Newton and quasi-Newton methods for solving these equations. Math. Oper. Res. 22(2), 301–325 (1997). https://doi.org/10.1287/moor.22.2.301 Article MathSciNet MATH Google Scholar Qi, L., Sun, ...
A primal-dual interior point algorithm for solving general nonlinear programming problems is presented. The algorithm solves the perturbed optimality conditions by applying a quasi-Newton method, where the Hessian of the Lagrangian is replaced by a positive definite approximation. An approximation of ...
The approximation is done with the BFGS matrix, in the spirit of quasi-Newton methods. The algorithm is admittedly heuristic, in that we do not provide a convergence proof; algorithms that drop cuts, as this one, are notoriously difficult to analyze. The use of “quasi-Jacobian”, temporary...
As an example where optimization could be added to further improve the solution’s accuracy for larger cut sizes, we used a standard quasi-Newton numerical optimization method to improve the error in the range ofL ∈ [a/4,a/2], i.e. roughly the half-domain where the original formula...
For these step size rules, local and quadratic convergence of the Newton method and local and superlinear convergence of the quasi-Newton method are proved. 展开 关键词: interior point method local convergence nonlinear programming DOI: 10.1007/BF02592190 被引量: 245 ...
[36], has been generalized to manifold-valued image processing tasks and employs a quasi-Newton method. Finally, the parallel Douglas–Rachford algorithm (PDRA) was introduced on Hadamard manifolds [13] and its convergence proof is, to the best of our knowledge, limited to manifolds with ...
However, for complex spectra, the relationship to combinatorics is lost, as we cannot, for example, talk about Newton polygons. We have chosen to stay in the real world as this is the most interesting case for applications. 2 Prelude: Gale duality and the Horn–Kapranov uniformization In ...
X1 X2 Y1 (%) Y2 (%) Y3 (Newton) Run (Ratio) (%) Observed Predicted Observed Predicted Observed Predicted F1 1:2 10 64.91 64.91 20.0 17.22 804.0 793.27 F2 1:1 10 72.7 72.7 25.0 31.38 715.0 771.44 F3 1:1 0 91.4 91.4 150.0 126.38 218.0 191.77 F4 2:1 5 85.8 85.8 100.0 92.22 ...