从此联立方程中可以直接求得x和λ的增量(primal-dual法),也可仅以x为自变量,靠迭代求解λ的增量(primal算法)。 * 令 r=rγ , 回到上一步更新x和λ,直到r趋于0。 2. 算法评价 2.1 算法评价基准 评价一个数值算法的基本判据有 * 精度* 收敛性* 计算量* 内存使用量* 并行算法的相容性 对于有限元计算...
Namely, we show that (i) the sequence of dual problems is convex and (ii) the dual values monotonically increase to the optimal primal value. We use these properties to devise a subgradient based primal鈥揹ual method, and show that the generated primal sequence accumulates at a solution of ...
Stationarity: dual problem中的最小值问题会在梯度为0的地方求得：∇f(x)+λ∇g(x)=0 Primal ...
We present a primal-dual augmented Lagrangian method for solving an equality constrained minimization problem, which is able to rapidly detect infeasibility. The method is based on a modification of the algorithm proposed in [1]. A new parameter is introduced to scale the objective function and, ...
The left hand side of (1.2) poses the primal problem. 1.3 Strong Lagrangian We say that P(b) is Strong Lagrangian if there exists λ such that φ(b) = inf x∈X L(x, λ) . (1.3) In other words, P(b) is Strong Lagrangian if it can be solved by the Lagrangian method. But wh...
Ngoc Nguyen Tran 576Accesses 2Citations Explore all metrics Abstract We present a primal-dual augmented Lagrangian method for solving an equality constrained minimization problem, which is able to rapidly detect infeasibility. The method is based on a modification of the algorithm proposed in Armand ...
The solution of the Lagrange dual is either the lower bound for the primal solution (for weak duality) or the exact primal solution (if conditions of strong duality are fulfilled). Lagrangian optimization with KKT conditions: The Lagrangian method is applicable when the constraint function is ...
(10) based on the gap between the best-known primal Z∗ and dual bound Zλnk. scale in Eq. (10) is an adjustable parameter in 0 < scale < 2, which is often set via trial and error. To achieve tighter bounds efficiently, Zeng and Cremaschi (2020) proposed updating scale at the ...
We show that any limit point of the primal ALCC iterates is an optimal solution of the conic convex problem, and the dual ALCC iterates have a unique limit point that is a Karush-Kuhn-Tucker (KKT) point of the conic program. We also show that for any epsilon>0, the primal ALCC ...
A new augmented Lagrangian primal dual algorithm for elastica regularization Regularization is a key element of variational models in image processing. To overcome the weakness of models based on total variation, various high order ... J Zhang,C Ke - 《Journal of Algorithms & Computational Technolog...