Decomposition algorithms for quasi-variational inequalities and generalized Nash equilibrium problems

Anno
2019
Proponente Simone Sagratella - Professore Associato
Sottosettore ERC del proponente del progetto
PE1_19
Componenti gruppo di ricerca
Componente Categoria
Francisco Facchinei Componenti strutturati del gruppo di ricerca
Marianna De Santis Componenti strutturati del gruppo di ricerca
Marco Boresta Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca
Abstract

Some decomposition methods were proposed for variational inequalities (VIs) and Nash equilibrium problems (NEPs), but there is almost none about their more general and powerful versions: quasi-variational inequalities (QVIs) and generalized Nash equilibrium problems (GNEPs). For this reason we want to develop new decomposition algorithms for QVIs and GNEPs:

- We intend to generalize a recently proposed augmented Lagrangian method for QVIs and GNEPs in order to make it suitable for parallel computing. The applicability of this method is subject to monotonicity of the inner VIs/NEPs, and can be obtained for some classes of problems.

- We want to develop a fast decomposition method for QVIs and GNEPs that exploits a penalization approach to compute a solution by means of a sequence of gradient projection iterations. Specifically, relaxing the coupling constraints, each gradient projection iteration can be performed in parallel by resorting to a Jacobi-type decomposition. We want to define assumptions for stong monotonicity of the obtained gradient projection operators to show complexity measures.

- We want to better investigate the convergence properties of some recently proposed gradient-type projection method for QVIs in order to enlarge the class of problems solvable with a distributed procedure. We also intend to consider inertial terms to speed-up these methods.

- We intend to develop a new active set block coordinate descent algorithm to compute stationary solutions of some QVI equation system reformulations.

Our decomposition methods will significantly improve the literature on QVIs and GNEPs. From a theoretical viewpoint, we will widen the classes of problems solvable with gradient-like and distributed methods. And we will prove new conditions for the absence of non-optimal stationary points for QVI equation system reformulations. From a practical viewpoint, our distributed methods will be very efficient and can be used to tackle big data applications.

ERC
PE1_19, PE6_6, PE1_17
Keywords:
OTTIMIZZAZIONE, PROGRAMMAZIONE NONLINEARE, ALGORITMI, CALCOLO PARALLELO E DISTRIBUITO, RICERCA OPERATIVA

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