Convergence analysis of modified pth power Lagrangian algorithms with alternative updating strategies for constrained nonconvex optimization

In this paper, we present new convergence properties of the primal-dual methods based on the pth power Lagrangian function for inequality-constrained nonconvex optimization problems. Convergence to a global optimal solution is first established for a basic primal-dual scheme under a mild condition, without requiring the boundedness condition of the multiplier sequence. Modified pth power Lagrangian methods based on three different algorithmic strategies are then proposed. We show that the same convergence of three modified algorithms can be ensured under weaker conditions. Finally, we present some preliminary numerical results for three modified pth power Lagrangian algorithms. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper introduces new convergence properties of primal-dual methods based on the pth power Lagrangian function for inequality-constrained nonconvex optimization problems. By proposing modified algorithms based on different strategies, the same convergence can be ensured under weaker conditions, providing a new approach for solving nonconvex optimization problems.