An interior point method with Bregman functions for the variational inequality problem with paramonotone operators

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

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A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

Fundamenta Informaticae ◽

10.3233/fi-2020-1983 ◽

2020 ◽

Vol 177 (2) ◽

pp. 141-156

Author(s):

Behrouz Kheirfam

Keyword(s):

Interior Point ◽

Interior Point Method ◽

Linear Optimization ◽

Point Method ◽

Central Path ◽

Interior Point Algorithm ◽

Positive Direction ◽

Complexity Result ◽

Infeasible Interior Point Method ◽

Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

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An interior point method for isogeometric contact

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2014.03.018 ◽

2014 ◽

Vol 276 ◽

pp. 589-611 ◽

Cited By ~ 18

Author(s):

İ. Temizer ◽

M.M. Abdalla ◽

Z. Gürdal

Keyword(s):

Interior Point ◽

Interior Point Method ◽

Point Method

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Correction to: A new full-Newton step interior-point method for P*(κ)-LCP based on a positive-asymptotic kernel function

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-021-01505-0 ◽

2021 ◽

Author(s):

Mingwang Zhang ◽

Kun Huang ◽

Mengmeng Li ◽

Yanli Lv

Keyword(s):

Kernel Function ◽

Interior Point ◽

Interior Point Method ◽

Point Method ◽

Newton Step ◽

Full Newton Step

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A Mean Extragradient Method for Solving Variational Inequalities

Symmetry ◽

10.3390/sym13030462 ◽

2021 ◽

Vol 13 (3) ◽

pp. 462

Author(s):

Apichit Buakird ◽

Nimit Nimana ◽

Narin Petrot

Keyword(s):

Hilbert Space ◽

Variational Inequality ◽

Weak Convergence ◽

Numerical Experiments ◽

Variational Inequality Problem ◽

Extragradient Method ◽

Mean Value ◽

Inequality Problem ◽

The Mean ◽

Mean Value Method

We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull of all previous iterates. We show weak convergence of the mean value iterate to a solution of the variational inequality problem, provided that a condition on the corresponding averaging matrix is fulfilled. Some numerical experiments are given to show the effectiveness of the obtained theoretical result.

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