Primal-dual gapGeneralized Bregman distanceDegeneracyresolventALTERNATING DIRECTION METHODPROXIMAL POINT ALGORITHMCONVERGENCE RATECONVEXWe revisit the operator splitting schemes proposed in a recent work of [Some extensions of the operator splitting schemes based on Lagrangian and primal-dual: A unified ...
These equivalences enable O(1/T) convergence guarantees in terms of both their classic primal gap and a not previously analyzed dual gap for strongly convex optimization. Consequently, our theory provides these classic methods with simple, optimal stopping criteria and optimality certificates at no ...
[Hpd(x)Dh(x)TAT−diag(u)Dh(x)−diag(h(x))0A00](ΔxΔuΔv)=−(rdualrcentrprim) 其中Hpd(x)=∇2f(x)+∑i=1mui∇2hi(x) 在IPM中我们定义surrogate duality gap:\eta=-h(x)^{T} u=-\sum_{i=1}^{m} u_{i} h_{i}(x),它将是我们迭代过程中的一个终止条件。
gap=np.zeros((max_it,)) primal[0]=p_nrg dual[0]=d_nrg y=forward_gradient(x) foritinrange(max_it): # Dual update y=y+sigma*forward_gradient(x_tilde) y=proximal_linf_ball(y,1.0) # Primal update x_old=x x=(x+tau*backward_divergence(y)+lambda_rof*tau*img_obs)/(1.0+lambda...
理论文章,对于CMDP的primal-dual方法,作者采用自然梯度法来更新原问题(参数theta),用投影的次梯度法来更新对偶变量(参数为lambda),在策略参数化使用softmax形式的玻尔兹曼分布时,能以1/sqrt(T)的速率抵达最优值,即使目标函数非凹约束条件非凸。 又证明了在使用光滑策略类时,由于函数估计误差,最优值存在对偶间隙,能...
Primal-dual interior-point methods (IPMs) have shown their power in solving large classes of optimization problems. However, at present there is still a gap between the practical behavior of these algorithms and their theoretical worst-case complexity results, with respect to the strategies of ...
For that, we need to find a feasible solution to a certain dual problem. 2 Thus, computability of ˆ f k (D) implies that we are able to point out a dual solution. And convergence of the primal-dual gap ¯ f k (D) − ˆ f k to zero implies that the dual solution ...
The convergence of our method is established not only in terms of the solution's distance to optimality but also in terms of the primal-dual objective gap. When applied to the data matrix factorized as a product of two smaller matrices, we show that the proposed method has a lower overall...
Further, combined with the conjugate theory, the zero duality gap properties between the pairs of Wolfe and Mond-Weir type primal-dual problems are ... Y Xu,S Li - 《Mathematics》 被引量: 0发表: 2022年 加载更多来源出版社 Springer Berlin Heidelberg 2001/01/01 研究点推荐 Primal-Dual Pairs...
因此我们可以用下面的对偶间隔(duality gap)衡量到合法解的距离: \Delta_{\Phi}=\Phi\left(\vec{x}^{\circ}, \vec{y}^{\circ}\right)-\Phi(\vec{x}, \vec{y}) \\ Anchor机制 具体如何求 \Pi_{\mathcal{C}}(\vec{x},\vec{y}) 呢?我们换种方式想,记: \left(\vec{x}^{\circ}, \...