非线性二阶锥优化问题的一种增广Lagrange算法的收敛性

Convergence Analysis of a Nonlinear Lagrange Method for Optimization Problems over Nonlinear Second-order Cones

基于与不等式约束优化问题的一个势函数相应的L?wner算子,建立了一个求解非线性二阶锥优化问题的增广Lagrange算法.分析了L?wner算子及相应增广Lagrange函数的微分性质,并在一些适当的假设条件下详细证明了增广Lagrange算法的收敛速度.

This paper proposes a nonlinear Lagrangian based on a L?wner operator associated with a potential function of the optimization problems with inequality constrains for solving nonlinear second-order cone programming problem.The properties of the operator and the nonlinear Lagrangian are discussed.And the paper analyzes the rate of convergence of the nonlinear Lagrange method under a set of suitable conditions.