论文标题
开发解决结构优化问题的方法
Development of a method for solving structural optimization problems
论文作者
论文摘要
实际上，优化任务具有一些结构，可以为每个问题开发新算法，并以更快的收敛速率开发。使用优化任务的结构，我们可以针对以下优化问题提出具有更乐观的收敛速率的算法：具有持有人连续梯度的功能，功能的叠加（最低最大问题），运输问题，运输问题，按选举模型进行集群。在这项工作中，我们将梯度类型方法统一使用不精确模型的特殊概念将梯度型方法统一到一种方法中，并开发一系列方法可以解决广义优化问题陈述，并借助提出的不精确模型概念来利用其结构。我们构建了相对平滑度，原始 - 双重自适应梯度和快速梯度方法的问题的梯度方法，以及支持函数不精确模型的随机非适应性梯度方法。此外，不精确模型的概念得到了优化问题的不同示例。
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence rates for the following optimization problems: functions with Holder continuous gradients, superposition of functions (min-max problems), transportation problems, clustering by electorial model. In this work, we propose the unification of gradient-type methods into one method using a special concept of inexact model and develop a series of methods that can solve generalized optimization problem statements and use its structure with the aid of the proposed concept of inexact model. We constructed the gradient method for problems with relative smoothness, the primal--dual adaptive gradient and fast gradient methods, and the stochastic nonadaptive gradient methods that support an inexact model of a function. Moreover, the concept of inexact model is supported by different examples of optimization problems.
