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The rate of convergence of proximal method of multipliers for nonlinear programming

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We analyze the rate of convergence of the proximal method of multipliers for non-convex nonlinear programming problems. First, we prove, under the strict complementarity condition, that the rate of convergence… Click to show full abstract

We analyze the rate of convergence of the proximal method of multipliers for non-convex nonlinear programming problems. First, we prove, under the strict complementarity condition, that the rate of convergence of the proximal method of multipliers is linear and the ratio constant is proportional to 1/c when the ratio is small enough, which implies that the rate of convergence of the proximal method of multipliers is superlinear when the parameter c increases to . Second, we prove that, without strict complementarity condition, the rate of convergence of the proximal method of multipliers is proportional to 1/c when c exceeds a threshold.

Keywords: rate convergence; method multipliers; proximal method; convergence proximal

Journal Title: Optimization Methods and Software
Year Published: 2020

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