Nesterov’s 1983 first-order minimization algorithm is equivalent to the numerical solution of a second-order ODE with non-constant damping. It is known that the algorithm can be obtained by time discretization with asynchronous damping, a long-standing technique in computational explicit dynamics. We extend the solution of the ODE to other time discretization algorithms, analyze their properties and provide an engineering interpretation of the process as well as a prototype implementation, addressing the estimation of the relevant parameters in the computational mechanics context. The main result is that a standard Newmark-type time-integration finite element code can be adopted to perform classical optimization in mechanics. Standard FE analysis, sensitivity analysis and optimization are performed in sequence using a typical FE framework. Geometric nonlinearities in the conservative case are addressed by the adjoint-variable method and examples of optimal fiber orientation are shown, exhibiting remarkable advantages with respect to more traditional optimization algorithms.

Nesterov 1983年的一阶最小化算法等效于具有非恒定阻尼的二阶ODE的数值解。众所周知，该算法可以通过使用异步阻尼的时间离散化来获得，异步阻尼是计算显式动力学中的一种长期存在的技术。我们将ODE的解决方案扩展到其他时间离散化算法，分析它们的属性，并提供过程的工程解释以及原型实现，以解决计算力学环境中相关参数的估计问题。主要结果是可以采用标准的Newmark型时间积分有限元代码来进行经典的力学优化。使用典型的有限元框架按顺序执行标准有限元分析，灵敏度分析和优化。