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Solving a class of semi-infinite variational inequality problems via a homotopy method

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Abstract

In this paper, the homotopy method is applied to solve a class of semi-infinite variational inequality problems with the complex structure, and the existence and convergence of the homotopy path are proved under non-monotonicity assumptions for the proposed mapping F. The numerical results of the algorithm also show that the homotopy method is robust and competitive for solving this class of semi-infinite variational inequality problems by comparing with inexact cutting plane method.

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Abbreviations

KKT:

Karush–Kuhn–Tucker

VIP:

Variational inequality problem

SIVIP:

Semi-infinite variational inequality problem

MFCQ:

Mangasarian–Fromovitz constraint qualification

\(R^{n}\) :

n dimensional Euclidean space

\(R_+^{n}\) :

The nonnegative orthant of \(R^{n}\)

\(R_{++}^{n}\) :

The positive orthant of \(R^{n}\)

VI(X, F):

VIP defined by the set X and the mapping F

\(\phi ^{-1}\) :

The inverse of a mapping \(\phi \)

\(S_1\backslash S_2\) :

The difference of two sets \(S_1\) and \(S_2\)

IT :

The number of iterations

\(\mathbf{CPU}\) :

The running time of the procedure in seconds

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Authors and Affiliations

  1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, Jiangsu, People’s Republic of China

    Xiaona Fan, Changhui Yu & Yan Chen

Authors
  1. Xiaona Fan
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  2. Changhui Yu
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  3. Yan Chen
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Corresponding author

Correspondence to Xiaona Fan.

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Communicated by José R Fernández.

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The work is supported by Foundation of NJUPT under Grant NY217097, NY218061, NY218079 and the Natural Science Foundation of China under Grant No. 11671004.

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Fan, X., Yu, C. & Chen, Y. Solving a class of semi-infinite variational inequality problems via a homotopy method. Comp. Appl. Math. 40, 288 (2021). https://doi.org/10.1007/s40314-021-01680-7

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  • DOI: https://doi.org/10.1007/s40314-021-01680-7

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