一种用于非线性约束优化的线搜索过滤序列自适应三次正则化算法
A line search filter sequential adaptive cubic regularisation algorithm for nonlinearly constrained optimization
AI总结：
本文提出一种线搜索过滤序列自适应三次正则化算法，通过复合步与投影矩阵处理非线性等式约束，并利用过滤技术避免罚参数选择困难，证明了全局收敛性并给出数值验证。
摘要：
本文提出了一种使用三次正则化的序列自适应正则化算法（ARC），用于求解非线性等式约束优化问题。该算法的动机来源于序列二次规划方法中处理约束的思想。在每次迭代中，我们采用复合步方法将新步分解为法向步与切向步之和。利用投影矩阵，我们将带约束的ARC子问题转化为一个标准的ARC子问题，从而生成切向步。在计算出新步之后，我们采用线搜索过滤技术来生成下一个迭代点。线搜索过滤技术使算法能够避免在价值函数中选择合适罚参数的困难，也避免了在ARC框架中一次迭代内多次求解ARC子问题的可能性。在一些温和假设下分析了算法的全局收敛性。报告了初步数值结果和比较。
英文摘要：
In this paper, a sequential adaptive regularization algorithm using cubics (ARC) is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic programming methods. In each iteration, we decompose the new step into the sum of the normal step and the tangential step by using composite step approaches. Using a projective matrix, we transform the constrained ARC subproblem into a standard ARC subproblem which generates the tangential step. After the new step is computed, we employ line search filter techniques to generate the next iteration point. Line search filter techniques enable the algorithm to avoid the difficulty of choosing an appropriate penalty parameter in merit functions and the possibility of solving ARC subproblem many times in one iteration in ARC framework. Global convergence is analyzed under some mild assumptions. Preliminary numerical results and comparison are reported.
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