Rate of Convergence for some constraint decomposition methods for nonlinear variational inequalities

2003 ◽  
Vol 93 (4) ◽  
pp. 755-786 ◽  
Author(s):  
Xue-Cheng Tai
Keyword(s):  
Variational Inequalities ◽  
Rate Of Convergence ◽  
Decomposition Methods ◽  
Constraint Decomposition

Remarks on the quasi-steady one phase Stefan problem

1986 ◽  
Vol 102 (3-4) ◽  
pp. 263-275 ◽  
Author(s):  
Bento Louro ◽  
José-Francisco Rodrigues
Keyword(s):  
Free Boundary ◽  
Variational Inequalities ◽  
Specific Heat ◽  
Rate Of Convergence ◽  
Stefan Problem ◽  
Free Boundaries ◽  
Variational Solutions ◽  
The One ◽  
Regularity Results ◽  
Boundary Estimates

SynopsisThis paper presents some regularity results on the solution and on the free boundary for the one phase Stefan problem with zero specific heat in the framework of the variational inequalities formulation. In particular we show the Hölder continuity of the free boundary. Estimates on the rate of convergence when the specific heat vanishes are given for the variational solutions and for the free boundaries.

scholarly journals Forward-reflected-backward method with variance reduction

2021 ◽  
Author(s):  
Ahmet Alacaoglu ◽  
Yura Malitsky ◽  
Volkan Cevher
Keyword(s):  
Variational Inequalities ◽  
Rate Of Convergence ◽  
Variance Reduction ◽  
Almost Sure Convergence ◽  
Ergodic Average ◽  
Strong Monotonicity ◽  
Monotone Variational Inequalities ◽  
Monotone Inclusions ◽  
Bregman Projections

AbstractWe propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a solution. In the monotone case, the ergodic average converges with the optimal O(1/k) rate of convergence. When strong monotonicity is assumed, the algorithm converges linearly, without requiring the knowledge of strong monotonicity constant. We finalize with extensions and applications of our results to monotone inclusions, a class of non-monotone variational inequalities and Bregman projections.

A class of Benders decomposition methods for variational inequalities

2019 ◽  
Vol 76 (3) ◽  
pp. 935-959 ◽  
Author(s):  
Juan Pablo Luna ◽  
Claudia Sagastizábal ◽  
Mikhail Solodov
Keyword(s):  
Variational Inequalities ◽  
Benders Decomposition ◽  
Decomposition Methods

SINGULAR PERTURBATION AND INTERPOLATION

1994 ◽  
Vol 04 (04) ◽  
pp. 557-570 ◽  
Author(s):  
C. BAIOCCHI ◽  
G. SAVARÉ
Keyword(s):  
Singular Perturbation ◽  
Variational Inequalities ◽  
Rate Of Convergence ◽  
Singular Perturbations ◽  
Convex Sets ◽  
Linear Interpolation ◽  
Interpolation Theory ◽  
Definition Of ◽  
Unperturbed Equation

It is well known that the rate of convergence of the solution uε of a singular perturbed problem to the solution u of the unperturbed equation can be measured in terms of the “smoothness” of u; smoothness which, in turn, can be expressed in terms of linear interpolation theory. We want to prove a closer relationship between interpolation and singular perturbations, showing that interpolate spaces can be characterized by such a rate of convergence. Furthermore, with respect to a suitable (quite natural) definition of interpolation between convex sets, such a characterization holds true also in the framework of variational inequalities.

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