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From Representation Theorems to Variational Inequalities

In: Computational Mathematics and Variational Analysis

Author

Listed:
  • Muhammad Aslam Noor

    (COMSATS University Islamabad)

  • Khalida Inayat Noor

    (COMSATS University Islamabad)

Abstract

We start with an historical introduction and then give an overview of the most important representation theorems for the linear(nonlinear) continuous functionals by the bifunction. Then we extensively study representations theorems for nonlinear operators. These representation results contain the difference of two(more) monotone operators, complementarity problems, systems of the absolute values equations and difference of two convex functions as special cases. These problems are very important and significant, which provide a unified and general framework of studying a wide class of unrelated problems.

Suggested Citation

  • Muhammad Aslam Noor & Khalida Inayat Noor, 2020. "From Representation Theorems to Variational Inequalities," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Computational Mathematics and Variational Analysis, pages 261-277, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-44625-3_15
    DOI: 10.1007/978-3-030-44625-3_15
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