In this paper, we present two inexact scalarization proximal point methods to solve quasiconvex multiobjective minimization problems on Hadamard manifolds. Under standard assumptions on the problem, we prove that the two sequences generated by the algorithms converge to a Pareto critical point of the problem and, for the convex case, the sequences converge to a weak Pareto solution. Finally, we explore an application of the method to demand theory in economy, which can be dealt with using the proposed algorithm.

中文翻译：

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Hadamard 流形上多目标拟凸面极小化的不精确近点方法

在本文中，我们提出了两种不精确标量化近端方法来解决 Hadamard 流形上的拟凸多目标最小化问题。在问题的标准假设下，我们证明算法生成的两个序列收敛到问题的帕累托临界点，对于凸情况，序列收敛到弱帕累托解。最后，我们探索了该方法在经济需求理论中的应用，可以使用所提出的算法进行处理。