关于B-不变凸约束优化问题解集的刻画

On characterizing solution sets of constrained B-invex optimization problems

给出了不同的带不等式约束的B-不变凸优化问题的最优解集的刻画,其结果用梯度和拉格朗日乘子表示。首先,证明了带不等式约束的B-不变凸优化问题的可行域和最优解集都是不变凸集,其次,建立了B-不变凸优化问题的拉格朗日函数在最优解集中是常值函数,然后,利用该性质得到了一些拉格朗日乘子为基础的最优解集的刻画。

In this paper, various characterizations of optimal solution sets of B -invex optimization problems with inequality constraints are given. The results are expressed in terms of gradients and Lagrange multlipliers. First, we prove that the feasible sets and the optimal solution sets of B -invex optimization problems with inequality constraints are invex. Second, we establish the Lagrangian function of B -invex optimization problems is constant function on the optimal solution sets. The property is then used to derive some.