New computable algorithms for smooth multiobjective optimization problems
该文提出求解光滑多目标优化问题的新算法，用线性规划找联合下降方向，证明收敛到弱帕累托最优，对经济学等多目标决策研究有参考价值。
We propose new practical algorithms for solving smooth multiobjective optimization problems based on determining joint decreasing directions via suitable linear programming problems. The presented iterative method is specialized for unconstrained, sign constrained and linearly constrained multiobjective optimization problems. In all cases we show that the objective function values sequence is decreasing with respect to the considered nonnegative orthant while the iterates are feasible. Furthermore, we prove that every accumulation point of the sequence generated by the algorithm, if any, is a substationary point to the considered multiobjective optimization problem, and, under convexity assumptions, it is actually a weakly Pareto efficient (also known as weakly Pareto-optimal) point. Different to similar algorithms from the literature, the ones proposed in this work involve joint decreasing directions that are easily computable in polynomial time by solving linear programming problems. The computational performance of our algorithms has been illustrated on convex unconstrained and convex linearly constrained multiobjective optimization problems.