Journal of Convex Analysis 34 (2027), No. 1, 103--127
Copyright Heldermann Verlag 2027
Relaxed Lagrangian Approach to First-Order Non-Convex Mean Field Type Control Problems
Cristian Mendico
Institut de Mathématique, Université Bourgogne, Dijon, France
cristian.mendico@u-bourgogne.fr
Kaizhi Wang
School of Mathematical Sciences, Jiao Tong University, Shanghai, China
kzwang@sjtu.edu.cn
Yuchen Xu
School of Mathematical Sciences, Jiao Tong University, Shanghai, China
math_rain@sjtu.edu.cn
We address the existence of equilibria for mean field type control problems of first-order with non-convex action functional. Introducing a relaxed Lagrangian approach on the Wasserstein space to handle the lack of convexity, we prove the existence of new relaxed Nash equilibria and we show that our existence result encompasses the classical Mean Field Control problem's existence result under convex data conditions.
Keywords: Mean field control, relaxed Lagrangian approach, relaxed controls, residual neural networks.
MSC: 49N80, 49N90, 68T07, 93C10.
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