关于双稳定束方法对偶问题的研究

对于带有非线性约束优化问题,本文在迫近束方法的思想基础上将水平束方法与其结合,应用双稳定束方法解决此优化问题.本文不仅从其对偶问题的角度研究了解的形式及相关性质,发现解的表现形式不尽相同,而且得出该解与之前迭代点的次梯度的凸组合有关的结论.进一步我们发现次梯度值和额定下降具有与单纯用迫近束方法从对偶问题角度解无约束优化问题相类似性质.

Research on the Dual Problem of Doubly Stabilized Bundle Method For Convex Optimization

For nonlinear constraint optimization problem,we try to solve it using doubly stabilized bundle method by combining the proximal bundle method with the level bundle method. This paper studies the form and the corresponding properties of the solution of subproblem from the viewpoint of the dual problem,finds that the forms of the solution are not similar,and comes to the conclusion that the solution is related to the convex combinations of the subgradient of the previous iteration. Furthermore,we find that the subgradients and the prediction descent have similar properties with the case in which we simply use the proximal bundle method to solve the unconstrained optimization problems from the point of view of dual problem.