Nonlinear Contraction Tools for Constrained Optimization

Abstract

This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly time-varying constraints. The paper formalizes the intuition that, just as convexity rather than linearity is the key property in optimization, contraction rather than linearity is the key dynamical property in this context.