非线性约束优化一个强收敛的广义投影强次可行方向法

A generalized projection of strongly sub-feasible direction method with strong convergence for nonlinear constrained optimization

讨论带非线性不等式和等式约束的最优化问题,借助强次可行方向法和半罚函数的思想,给出了问题的一个新的广义投影强次可行方向法.该算法的一个重要特性是有限次迭代后,迭代点落入半罚问题的可行域.在适当的条件下证明了算法的全局收敛性和强收敛性.数值实验表明算法是有效的.

In this paper, the optimization problems with nonlinear inequality and equality constraints are discussed. With the help of strongly sub-feasible direction method and the idea of semipenalty function, a new generalized projection of strongly sub-feasible direction method for the discussed problems is proposed. An outstanding property of the proposed algorithm is that the iteration points can enter into the feasible region of the semi-penalty problem after a finite number of iterations. Under some suitable conditions, the globally and strongly convergent properties are obtained. The numerical experiments show that the proposed algorithm is promising.