论文标题
连续方法与可信赖的时间步长方案，用于线性约束优化，并使用嘈杂的数据进行线性约束
Continuation Method with the Trusty Time-stepping Scheme for Linearly Constrained Optimization with Noisy Data
论文作者
论文摘要
线性约束的非线性优化问题在工程领域中具有许多应用，例如视觉惯用导航和无人驾驶飞机维护水平飞行的定位。为了有效地解决这个实用问题，本文使用可信赖的时间步态方案构建了一种延续方法，用于在每个采样时间在线性相等受限的优化问题。在每次迭代中，新方法仅求解除传统优化方法（例如顺序二次编程（SQP）方法）以外的线性方程系统，该方法需要求解二次编程子问题。因此，与SQP相比，新方法可以节省更多的计算时间。数值结果表明，新方法可用于此问题，其消耗时间约为SQP（MATLAB2018A环境的内置subroutine fmincon.m）或传统动力学方法（MATLAB2018A环境的内置subroutine ode15s.m）的五分之一。此外，我们还提供了新方法的全球收敛分析。
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to solve this practical problem efficiently, this paper constructs a continuation method with the trusty time-stepping scheme for the linearly equality-constrained optimization problem at every sampling time. At every iteration, the new method only solves a system of linear equations other than the traditional optimization method such as the sequential quadratic programming (SQP) method, which needs to solve a quadratic programming subproblem. Consequently, the new method can save much more computational time than SQP. Numerical results show that the new method works well for this problem and its consumed time is about one fifth of that of SQP (the built-in subroutine fmincon.m of the MATLAB2018a environment) or that of the traditional dynamical method (the built-in subroutine ode15s.m of the MATLAB2018a environment). Furthermore, we also give the global convergence analysis of the new method.
