A Primer in Optimization

With a Focus on Microeconomics

This tiny book presents the theory of optimization for mathematical programming problems: the minimization of functions defined on Rⁿ subject to a finite number of equality and inequality constraints.

Mauricio 'Pacha' Vargas Sepúlveda

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About the Book

This tiny book presents the theory behind Karush-Kuhn-Tucker (KKT) conditions and how to solve minimization and maximization problems for differentiable functions defined on Rⁿ subject to a finite number of equality and inequality constraints. I tried to explain KKT conditions and duality beyond just solving the Lagrangian. I worked on direct explanations about the Hyperplane Separation Theorem, Farkas' Lemma, and the Envelope Theorem to connect mathematical notions to well-known micro results such as Roy's Identity and Shepard's Lemma for a straightforward interpretation of KKT multipliers as "shadow prices" and how changes in budgets and prices affect optimal decisions.

The goals are:

Cover what I consider are some gaps between Varian (1992) and/or Jehle (2011) compared to Mas-Colell (1995).
Provide a concise reference for students by presenting the results using consistent notation and terminology.
Provide a basis for more advanced topics in optimization, such as convex analysis and variational calculus.

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Mauricio 'Pacha' Vargas Sepúlveda

I am a PhD student in Political Science at the University of Toronto. My research interests include International Relations, Canadian Politics and Public Policy, with a focus on the politics of trade agreements and sanctions. I have a Master of Arts in Political Science from the University of Toronto, a Master of Science in Statistics from the Catholic University of Chile, and an Engineering degree from the University of Chile. I can provide my CV (academic/professional) upon request. You can reach me at m.sepulveda+removethis@mail.utoronto.ca (please remove the +removethis).

See my website (pacha.dev) and my blog (pacha.dev/blog).

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