论文标题
多目标优化及其属性的新功能
New merit functions for multiobjective optimization and their properties
论文作者
论文摘要
优点（GAP）函数是一个地图，在问题的解决方案和严格的正值否则下返回零。根据定义，它的最小化等效于原始问题，并且可以估计给定点和解决方案集之间的距离。理想情况下，此函数应具有一些属性，包括易于计算，连续性，可不同，级别设置的界限和误差界限。在这项工作中，我们提出了新的优点功能，以使用较低的半连续目标，凸目标和复合目标来进行多目标优化，并且我们表明它们在合理的假设下具有如此理想的属性。
A merit (gap) function is a map that returns zero at the solutions of problems and strictly positive values otherwise. Its minimization is equivalent to the original problem by definition, and it can estimate the distance between a given point and the solution set. Ideally, this function should have some properties, including the ease of computation, continuity, differentiability, boundedness of the level set, and error boundedness. In this work, we propose new merit functions for multiobjective optimization with lower semicontinuous objectives, convex objectives, and composite objectives, and we show that they have such desirable properties under reasonable assumptions.
