2 citations · 3 across the 6 of their papers we have counts for
6 papers
Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum monotone operators
Patrick L. Combettes, Jean-Christophe Pesquet
We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian oper…
Monotone Operator Methods for Nash Equilibria in Non-Potential Games
Luis M. Briceno-Arias, Patrick L. Combettes
We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve…
Moreau's Decomposition in Banach Spaces
Patrick L. Combettes, Noli N. Reyes
Moreau's decomposition is a powerful nonlinear hilbertian analysis tool that has been used in various areas of optimization and applied mathematics. In this paper, it is extended t…
A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality
L. Briceno-Arias, P. L. Combettes
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduce…
Functions with Prescribed Best Linear Approximations
P. L. Combettes, N. N. Reyes
A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present…
A parallel splitting method for weakly coupled monotone inclusions
H. Attouch, L. M. Briceno-Arias, P. L. Combettes
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlik…