Abstract

In this paper, we study the optimization problem (PWE) of minimizing a convex function over the set of weakly efficient solutions of a convex multiobjective problem. This is done by using the fact that each lower semicontinuous convex function is an upper envelope of its affine minorants together with a generalized cutting plane method. We give necessary conditions for optimal solutions of the problem $(\mathit{PWE}).$ Moreover, a novel algorithm for solving the problem (PWE) together with numerical results are presented. We also prove that the proposed algorithm terminates after a finite numbers of iterations, and the algorithm is coded in MATLAB language and evaluated by numerical examples.

摘要

在本文中，我们研究了在凸多目标问题的弱有效解集上最小化凸函数的优化问题（PWE）。这是通过以下事实完成的：每个下半连续凸函数是其仿射少数的上包络以及广义剖切面方法。我们为问题的最佳解决方案提供了必要的条件$（\mathit{PWE}）。$此外，提出了一种解决该问题的新算法（PWE），并给出了数值结果。我们还证明了该算法在有限次迭代后终止，并且该算法用MATLAB语言进行了编码并通过数值示例进行了评估。