An Implicit Smoothing-enabled Algorithm for Strongly Convex Stochastic Multiobjective Optimization with Equilibrium Constraints

Stochastic multiobjective optimization has at-tract widespread attention in real-world scenarios. However, the current work mainly focuses on the gradient-based algorithms and there is a lack of effective methods for gradient-free problems. In this paper, we consider strongly convex stochastic multiobjective optimization problem with equilibrium constraints (SMOPEC) which may not be differ-entiable. By ultilizing a local spherical smoothing approxi-mation framework the zeroth-order method for this problem is presented, and the convergence analysis of the proposed algorithm is also provided under adequate assumptions. Finally, numerical experiment is conducted to verify the effectiveness of the proposed algorithm.