A Proximal Zeroth-Order Algorithm for Nonconvex Nonsmooth Problems
It addresses optimization for networked multi-agent systems where only noisy objective information is available, offering a method for scenarios where classical approaches fail, though it appears incremental as it builds on existing primal-dual and zeroth-order techniques.
The paper tackles nonconvex nonsmooth optimization problems common in networked systems like signal processing and distributed learning, proposing a proximal zeroth-order primal dual algorithm (PZO-PDA) that uses only functional values and proves convergence with rates, validated by numerical experiments.
In this paper, we focus on solving an important class of nonconvex optimization problems which includes many problems for example signal processing over a networked multi-agent system and distributed learning over networks. Motivated by many applications in which the local objective function is the sum of smooth but possibly nonconvex part, and non-smooth but convex part subject to a linear equality constraint, this paper proposes a proximal zeroth-order primal dual algorithm (PZO-PDA) that accounts for the information structure of the problem. This algorithm only utilize the zeroth-order information (i.e., the functional values) of smooth functions, yet the flexibility is achieved for applications that only noisy information of the objective function is accessible, where classical methods cannot be applied. We prove convergence and rate of convergence for PZO-PDA. Numerical experiments are provided to validate the theoretical results.