ABSTRACT

We propose and analyse a nonmonotone quasi-Newton algorithm for unconstrained strongly convex multiobjective optimization. In our method, we allow for the decrease of a convex combination of recent function values. We establish the global convergence and local superlinear rate of convergence under reasonable assumptions. We implement our scheme in the context of BFGS quasi-Newton method for solving unconstrained multiobjective optimization problems. Our numerical results show that the nonmonotone quasi-Newton algorithm uses fewer function evaluations than the monotone quasi-Newton algorithm.

中文翻译：

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无约束多目标优化的超线性收敛非单调拟牛顿法

摘要

我们提出并分析了一种用于非约束强凸多目标优化的非单调拟牛顿算法。在我们的方法中，我们允许减少最近函数值的凸组合。我们在合理的假设下建立了全局收敛性和局部超线性收敛速度。我们在BFGS拟牛顿法的背景下实施我们的方案，以解决无约束的多目标优化问题。我们的数值结果表明，非单调拟牛顿算法比单调拟牛顿算法使用更少的函数求值。