On the stability of Maslov optimization processes

This paper examines the stability of nonlinear systems involving optimization variables. The approach develops some natural Liapunov functions for the study of optimization processes in the same way as stochastic Liapunov functions for Markov stochastic processes. More precisely, an optimization Liapunov function is defined as a suitable function of the state of an optimization process in the sense of Maslov (1986, 1987) which possesses the corresponding (max,+)-supermartingale property.