Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations
نویسندگان
چکیده
منابع مشابه
Augmented Lagrangian Methods for Transport Optimization, Mean-field Games and Degenerate Pdes
Many problems from mass transport can be reformulated as variational problems under a prescribed divergence constraint (static problems) or subject to a time dependent continuity equation which again is a divergence constraint but in time and space. A large class of Mean-Field Games introduced by Lasry and Lions may also be interpreted as a generalisation of the time-dependent optimal transport...
متن کاملAugmented Lagrangian Methods and Proximal Point Methods for Convex Optimization
We present a review of the classical proximal point method for nding zeroes of maximal monotone operators, and its application to augmented Lagrangian methods, including a rather complete convergence analysis. Next we discuss the generalized proximal point methods, either with Bregman distances or -divergences, which in turn give raise to a family of generalized augmented Lagrangians, as smooth...
متن کاملNonlinear Elliptic Systems and Mean Field Games ∗
We consider a class of quasilinear elliptic systems of PDEs consisting of N HamiltonJacobi-Bellman equations coupled with N divergence form equations, generalising to N > 1 populations the PDEs for stationary Mean-Field Games first proposed by Lasry and Lions. We provide a wide range of sufficient conditions for the existence of solutions to these systems: either the Hamiltonians are required t...
متن کاملAugmented Lagrangian and Total Variation Methods for Recovering Discontinuous Coeecients from Elliptic Equations
Estimation of coeecients of partial diierential equations is ill-posed. Output-least-squares method is often used in practice. Convergence of the commonly used minimization algorithms for the inverse problem is often very slow. By using the augmented Lagrangian method, the inverse problem is reduced to a coupled linear algebraic system, which can be solved eeciently. Total variation techniques ...
متن کاملMean Field Games: Numerical Methods
Mean field type models describing the limiting behavior of stochastic differential game problems, as the number of players tends to +∞, have recently been introduced by J-M. Lasry and P-L. Lions. Numerical methods for the approximation of stationary and nonstationary such models are proposed. In particular, existence and uniqueness are investigated, as well as bounds on the solutions. Numerical...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2015
ISSN: 0022-3239,1573-2878
DOI: 10.1007/s10957-015-0725-9