组合同伦方法在非凸优化问题上的应用

The Application of Homotopy Methods on Nonconvex Optimization Problem

借鉴已有的理论结果,研究具体一类非凸约束区域上优化问题的组合同伦方法的实现。针对这类非凸约束区域,给出了拟法锥的构造方法。证明了所选映射关于约束梯度是正独立的、可行域关于所选映射是满足拟法锥条件的,构造了拟法锥条件下的组合同伦方程,说明了同伦方法的可行性。

Drawing lessons from the ready theories results,deals with the achievement of optimization problem about combined homotopy interior point method on concrete a type of nonconvex constrained domain.Contraposing to this nonconvex constrained domain,we give the structure method of the quasi-normal.Prove the chosen mappings on constrained grads are positive independent,the chosed mapping on constrains feasible set satisfy the quasi-normal cone condition,and construct combined homotopy equation under the quasi-normal cone condition which shows the possibility of the Homotopy Methods.