鲁棒多目标优化问题的最优性和对偶性

Optimality and Duality for Robust Multiobjective Optimization Problems

针对非光滑、非凸实值函数的鲁棒多目标优化问题,建立鲁棒(弱)有效解的充分优化条件,并探索了对偶(鲁棒)多目标问题的强弱对偶关系;利用复合函数的极限次微分,凸性推广至(严格)广义伪凸的条件下仍能得到优化问题的最优性条件,并进一步通过对偶问题建立强弱鲁棒对偶性;最后在(严格)广义伪凸的条件之下,得到3个定理并加以证明。

For the robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions,the sufficient optimality conditions for robust( weakly) Pareto solutions are established. In addition,weak and strong duality relations of the dual multiobjective problem are explored. Using the limiting subdifferential of the compound function,the optimality condition of the optimization problem can still be obtained under the condition of( strictly) generalized pseudoconvex,and the strong and werk duality can be established by the dual problem.Finally,under the condition of( strictly) generalized pseudoconvex,three theorems are obtained and proved.