Kuhn–Tucker Conditions

Mikuláš Luptáčik () and Klaus Prettner
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Mikuláš Luptáčik: WU Vienna University of Economics and Business, Department of Economics

Chapter 2 in Mathematical Optimization and Economic Analysis, 2026, pp 31-66 from Springer

Abstract: 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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-0716-5076-9_2

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DOI: 10.1007/978-1-0716-5076-9_2

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