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论文类型：期刊论文

发表时间：2020-09-01

发表刊物：OPTIMIZATION LETTERS

收录刊物：SCIE

卷号：14

期号：6

页面范围：1599-1613

ISSN号：1862-4472

关键字：Equality constrained optimization; Rate of convergence; The proximal method of multipliers

摘要：The proximal method of multipliers was proposed by Rockafellar (Math Oper Res 1:97-116, 1976) for solving convex programming and it is a kind of proximal point method for convex programming. In this paper, we apply this method for equality constrained optimization problems, in which subproblems have better properties than those from the augmented Lagrange method. We prove that, under linear independence constraint qualification and the second-order sufficiency optimality condition, the rate of convergence of the proximal method of multipliers, for the equality constrained optimization problem, is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold c(*) > 0. Moreover, the rate of convergence of the proximal method of multipliers is superlinear when the parameter c increases to +infinity.