OPTIMIZATION WITH INEQUALITY CONSTRAINTS

Vasileios Zikos

Chapter 6 in Essential Mathematics for Economics:A Student's Guide to Key Mathematical Techniques, 2026, pp 89-105 from World Scientific Publishing Co. Pte. Ltd.

Abstract: After completing this chapter, students will be able to:Understand how methods of solving constrained optimization problems can be extended to include inequality constraints.Apply the Kuhn–Tucker conditions to solve optimization problems with inequality constraints.Recognize the circumstances under which the Kuhn–Tucker conditions are necessary and sufficient.Chapter 5 focused on optimization problems with equality constraints. Our main objective was to identify the extreme points of a function subject to one or more binding constraints. The current chapter extends these methods to address the more general case of inequality constraints. For example, a consumer may wish to spend some, but not all, of her budget, while a firm might utilize only a portion of its available resources. In both cases, the constraint functions are not satisfied as equalities…

Keywords: Microeconomics; Applied Microeconomics; Optimization; First-order Conditions; Second-order Conditions; Equality Constraints; Inequality Constraints; Concavity; Convexity; Matrix Algebra; Determinants; Differential Calculus; Integral Calculus; First-order Linear Differential Equations; Utility Maximization; Profit Maximization; Research Applications (search for similar items in EconPapers)
JEL-codes: C01 C02 C61 D00 (search for similar items in EconPapers)
Date: 2026
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