We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography, and economics. To solve these generally large-scale LP efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with easy-to-implement...

Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of the iterate to the solution leading thus to worst case estimates, i.e., how fast the algorithm must converge. Exact convergence estimates are typically hard t...

Abstract In this paper, we introduce and study a modified Halpern-type proximal point algorithm which comprises finite family of resolvents mixed equilibrium problems k -demimetric mappings. We prove that the converges strongly to common solution problems, is also fixed mappings in Hadamard space. Furthermore, give numerical example our show applicability algorithm.

Abstract In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in Pougkakiotis and Gondzio (Comput Optim Appl 78:307–351, 2021. 10.1007/s10589-020-00240-9 ) for solution linear positive Semi-Definite Programming (SDP) problems, allowing inexactness associated Newton systems. particular, combine an infeasible Point (IPM) with Proximal (PMM) interpret al...

We study stability properties of a proximal point algorithm for solving the inclusion 0 ∈ T (x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact pr...

This paper proposes a distributed algorithm for games with shared coupling constraints based on the variational approach and proximal-point algorithm. The demonstrates effectiveness of in computing generalized Nash equilibrium (GNE) problems using local data communication neighbors any networked game. achieves goal reflecting decisions Nash–Cournot game under partial-decision information while ...

A new monotonicity, M-monotonicity, is introduced, and the resolvant operator of an M-monotone operator is proved to be single-valued and Lipschitz continuous. With the help of the resolvant operator, the positively semidefinite general variational inequality (VI) problem VI (S+,F +G) is transformed into a fixed point problem of a nonexpansive mapping. And a proximal point algorithm is construc...