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Kuhn–Tucker Conditions

In: Mathematical Optimization and Economic Analysis

Author

Listed:
  • Mikuláš Luptáčik

    (WU Vienna University of Economics and Business, Department of Economics)

  • Klaus Prettner

    (WU Vienna University of Economics and Business, Department of Economics)

Abstract

This chapter develops necessary conditions for optimality in constrained optimization problems. Building on classical Lagrange theory, it introduces the Kuhn–Tucker conditions as a generalization applicable to inequality constraints. The chapter explores the rationale of the Kuhn–Tucker conditions and their relationship to a saddle point of the Lagrange function. It illustrates the main ideas through numerical examples, and shows their usefulness in qualitative economic analysis. Applications such as peak-load pricing, revenue maximization under various constraints, and the effects of different instruments of environmental regulation demonstrate how optimization techniques lead to powerful economic insights.

Suggested Citation

  • Mikuláš Luptáčik & Klaus Prettner, 2026. "Kuhn–Tucker Conditions," Springer Optimization and Its Applications, in: Mathematical Optimization and Economic Analysis, edition 0, chapter 2, pages 31-66, Springer.
    • Handle: RePEc:spr:spochp:978-1-0716-5076-9_2
    DOI: 10.1007/978-1-0716-5076-9_2
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