First-order primal–dual algorithmOS-SARTTotal variationSparse-viewNeutron computed tomography(NCT) is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics, and cultural
model. more precisely, applying an inexact primal–dual algorithm to formulation ( 1 ), we obtain a nested algorithm in the spirit of [ 6 , 7 , 20 , 30 , 33 , 59 , 61 ], $$\begin{aligned} y^{n+1}&= {{\mathrm {prox}}}_{\sigma h^*}(y^n + \sigma k_1(x^{n+1} ...
In this paper, we prove that the proposed algorithm con- verges with rate O(1/N) for the primal-dual gap. In [25], Nesterov showed that this rate of convergence is optimal for the class of convex optimization problems with known structure. Hence, our primal-dual algorithm is optimal in...
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization 热度: Experimental characterization and Monte Carlo simulation of Si(Li) detector efficiency by radioactive sources and PIXE 热度: Precise optical modeling of blue light-emitting diodes by Monte Carlo ray-tr...
在proximal algorithm的框架里,它也被称作prox(imal) function/prox(imal) term等等,因为它便是用来衡量两个点x,y的接近(proximity)程度的。D(x,y)有很多性质,如它也是strongly convex的(giveny),它不对称,D(x,y)\geq \frac{1}{2}\|x-y\|^2等等,更深层次的探讨可以见我之前的一个回答:...
dFeasToldouble>=01e-8Tolerance for primal and dual infeasibility check The PDLP Algorithm Consider the generic linear programming problem: minc⊤xs.t.Ax=bGx≥hl≤x≤u Equivalently, we solve the following saddle-point problem, maxy1,free,y2≥0minl≤x≤uc⊤x−y⊤Kx+q⊤y ...
Primal-Dual Hybrid Gradient (PDHG) algorithm takes the step as follows, xk+1=Πl≤x≤u(xk−τ(c−K⊤yk))yk+1=Πy2≥0(yk+σ(q−K(2xk+1−xk))) The termination criteria contain the primal feasibility, dual feasibility, and duality gap. ...
17、 algorithm that can find an first order Nash equilibrium forgeneral non-convex saddle point games remains open.Several recent results provided a partial answer to the problem of finding first-order stationary points of a non-convex min-max game. For instance, 51 proposed a stochastic gradient...
In this paper we study a first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rateO(1/N) in finite dimensions for the complete class of problems. We further show accelerations of the proposed...
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imag. Vision 40(1), 120–145 (2011). https://doi.org/10.1007/s10851-010-0251-1 8. Chambolle, A., Pock, T.: On the ergodic convergence rates of a first-...