An algorithm for solving the expectation formulation of stochastic nonsmooth multiobjective optimization problems is proposed. The proposed method is an extension of the classical stochastic gradient algorithm to multiobjective optimization using the properties of a common descent vector defined in the deterministic context. The mean square and the almost sure convergence of the algorithm are proven. The algorithm efficiency is illustrated and assessed on an academic example.
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Poirion, F., Mercier, Q. & Désidéri, J. Descent algorithm for nonsmooth stochastic multiobjective optimization. Comput Optim Appl 68, 317–331 (2017). https://doi.org/10.1007/s10589-017-9921-x
- Multiobjective optimization
- Almost sure convergence