Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

Abstract

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.

Keywords

Potential function / Löwner operator / augmented Lagrange algorithm / nonlinear second-order cone optimizations

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Higher Education Press