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Optimization With Inequality Constraints

In: ESSENTIAL MATHEMATICS FOR ECONOMICS A Student’s Guide to Key Mathematical Techniques

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  • VASILEIOS ZIKOS

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…

Suggested Citation

  • Vasileios Zikos, 2026. "Optimization With Inequality Constraints," World Scientific Book Chapters, in: ESSENTIAL MATHEMATICS FOR ECONOMICS A Student’s Guide to Key Mathematical Techniques, chapter 6, pages 89-105, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789819814114_0006
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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D00 - Microeconomics - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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