Intertwined escort dynamics: A dynamical framework for constrained optimization

Abstract

Feasibility-preserving algorithms with guaranteed convergence continue to pose challenges for constrained optimization, especially on larger scales or in distributed settings. Toward solving this problem, a well-founded mathematical framework named Intertwined Escort Dynamics (IED) is introduced, in which optimization takes the form of an interacting dynamical system described by escort maps. The framework ensures feasibility inherently at all stages of the process. With fixed-point analysis, it is proven that the resulting dynamics have equilibria that satisfy the Karush–Kuhn–Tucker (KKT) optimality conditions under general conditions. The proposed framework provides a clear bridge between evolutionary dynamics and constrained optimization, offering an algorithmic approach to obtaining an optimum without resorting to the traditional Lagrange multiplier-based approach. This capability has been verified using a number of optimization benchmarks and economic load dispatch in a large-scale scenario.