法锥条件下多目标规划问题的同伦内点解法

Homotopy Interior Method for General Multi-objective Programming Problem

本文提出了一种求解法锥假设条件下多目标规划问题的组合同伦内点方法.首先,建立了和多目标规划问题的KKT系统直接相联系的组合同伦方程.其次,在法锥条件下证明了从几乎所有的初始内点出发,达到多目标规划问题的KKT系统解的光滑同伦路径存在并且收敛.

In this paper, we present a combined homotopy interior-point method for a general multi-objective programming problem under norm cone assumptions. Firstly, a combined homotopy equation is constructed which is related to the KKT system directly. Secondly, we prove the existence and convergence of a smooth homotopy path from almost any initial interior point to a solution of the KKT system of the multi-objective programming problem under norm cone assumptions.