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Long-Step Interior-Point Algorithms for a Class of Variational Inequalities with Monotone Operators

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Abstract

This paper describes two interior-point algorithms for solving a class of monotone variational inequalities defined over the intersection of an affine set and a closed convex set. The first algorithm is a long-step path-following method, and the second is an extension of the first, incorporating weights in the gradient of the barrier function. Global convergence of the algorithms is proven under the assumptions of monotonicity and differentiability of the operator.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada

    F. Sharifi-Mokhtarian (PhD Student)

  2. Faculty of Management, McGill University, Montreal, Quebec, Canada

    J. L. Goffin (Professor)

Authors
  1. F. Sharifi-Mokhtarian
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  2. J. L. Goffin
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Sharifi-Mokhtarian, F., Goffin, J.L. Long-Step Interior-Point Algorithms for a Class of Variational Inequalities with Monotone Operators. Journal of Optimization Theory and Applications 97, 181–210 (1998). https://doi.org/10.1023/A:1022683302494

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  • DOI: https://doi.org/10.1023/A:1022683302494

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