论文标题
Bregman惯性前向反向回复方法，用于最小化
A Bregman inertial forward-reflected-backward method for nonconvex minimization
论文作者
论文摘要
我们提出了一种惯性惯性前向反向反复反过来（BIFRB）方法，以解决非凸复合问题。我们的分析依赖于一种新的方法，该方法将一般条件施加在隐式优点函数参数上，该参数产生了独立于惯性参数的步骤大小条件。反过来，解决了Malitsky和TAM是否可以解决FRB是否可以配备Nesterov型加速度。假设物镜的二次正则化的广义凹库伊卡西维奇属性，我们获得了BIFRB的顺序收敛，以及函数值和实际序列上的收敛速率。我们还为布雷格曼子问题提供了公式，不仅补充了Bifrb，还补充了Boţ-Csetnek-László和Boţ-Csetnek的作品。进行数值模拟以评估我们提出的算法的性能。
We propose a Bregman inertial forward-reflected-backward (BiFRB) method for nonconvex composite problems. Our analysis relies on a novel approach that imposes general conditions on implicit merit function parameters, which yields a stepsize condition that is independent of inertial parameters. In turn, a question of Malitsky and Tam regarding whether FRB can be equipped with a Nesterov-type acceleration is resolved. Assuming the generalized concave Kurdyka-Łojasiewicz property of a quadratic regularization of the objective, we obtain sequential convergence of BiFRB, as well as convergence rates on both the function value and actual sequence. We also present formulae for the Bregman subproblem, supplementing not only BiFRB but also the work of Boţ-Csetnek-László and Boţ-Csetnek. Numerical simulations are conducted to evaluate the performance of our proposed algorithm.
