论文标题
使用不精确梯度的非线性约束的多目标信任区域滤波器方法
Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients
论文作者
论文摘要
在本文中，我们以先前的工作为基础，为非线性约束多目标优化问题提供了优化算法。该算法将替代辅助的无衍生信任区域方法与单目标优化已知的滤波器方法结合在一起。采用了所谓的完全线性模型，而不是真正的目标和约束功能，我们还展示了如何在复合步骤设置中处理梯度不符合性，也适用于单目标优化。在标准假设下，我们证明了迭代的子集转到准平台点的收敛性，并且如果达到约束资格，则极限点也是多目标问题的KKT点。
In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed, and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem.
