【摘要】 基于一类非线性Lagrange函数提出不等式约束优化问题的一类对偶问题,证明了在Jacobian惟一条件下,对偶问题的最优解处二阶充分性条件是成立的,因此对偶解处满足二阶增长条件.非线性Lagrange函数的鞍点存在是原始问题与对偶问题无对偶间隙的充分条件,给出了鞍点条件的等价条件,并且给出了用扰动函数来刻画的鞍点存在的一个充分条件.更多还原

【Abstract】 Dual problems based on a class of nonlinear Lagrange functions for inequality constrained optimization problems are proposed.Under the Jacobian uniqueness conditions,the second order sufficient conditions for the dual problem are demonstrated so that the quadratic growth condition holds at the solution.The equivalence conditions for the existence of saddle points are given,which are sufficient for zero duality gap between the primal problem and the dual problem.Moreover,a sufficient condition for the existence of saddle points is presented,which is characterized by the perturbation function.更多还原