Optimization I

Operations Research, 2026-1

Syllabus del curso

Syllabus

Problem sets

Graded problem sets and solutions

Graded problem set 1

Solutions to problem sets

Exams

Mandatory book

Linear Algebra and Optimization for the Economic Analysis

Suggested books and sources

(1) For linear algebra: Linear Algebra Done Right 4h edition (Sheldon Axler, 2025), Linear Algebra 2nd Edition (Kenneth M Hoffman and Ray Kunze, 1971).
(2) For applied linear algebra: Mathematics for Economists (Carl P. Simon and Lawrence E. Blume, 1987)
(3) For topology in Rn: Mathematics for Economists (Carl P. Simon and Lawrence E. Blume, 1987), Analysis II fouth edition (Terence Tao, 2022).
(4) For convex analysis: Finite Dimensional Convexity and Optimization (Monique Florenzano, 2001), Matemáticas para el análisis económico (Uldarico Malaspina, 1994).
(5) For convex, concave functions: A first course in optimization (Raghu Sundaram, 1996), Mathematics for Economists (Carl P. Simon and Lawrence E. Blume, 1987).
(6) For static optimization: A first course in optimization (Raghu Sundaram, 1996), Mathematical Methods and Models for Economists (Angel de la Fuente, 2000), Mathematics for Economists (Carl P. Simon and Lawrence E. Blume, 1987).
(7) For consumer and prooducer theory: Microeconomic Theory (Mas-Colell et al., 1995), Microeconomic Foundations I (Kreps, 2013), Microeconomic Analysis (Varian, 1992).
(8) For general equilibrium: Microeconomic Theory (Mas-Colell et al., 1995), Existence and Optimality of Competitive Equilibria (Aliprantis et al., 1990).
(9) For game theory: A Course in Game Theory (Osborne and Rubinstein, 1994), Game Theory for Applied Economists (Robert Gibbons, 1992), Game Theory: Analysis of Conflict (Roger Myerson, 1991).
(10) ECON204 UC Berkeley, Chris Shannon course.
(11) For advanced study: Real Analysis with Economic Applications (Efe A. Ok, 2007), Mathematical Economics (Kevin Lancaster, 1968), Optimal Transport Methods in Economics (Algred Galichon, 2016), Optimization by Vector Spaces Methods (David G. Luenberger, 1969), Convex Optimization (Stephen Boyd, 2004).
(12) The Extraordinary Theorems of John Nash - with Cédric Villani. Cédric Villani was Fields Medal winner in 2010.
(13) Lecture Notes General Equilibrium Theory, by Professor Federico Echenique.
(14) For numerical optimization (not required for the course): Numerical Optimization (Nocedal and Wrigth, 2006), Optimization, Volume 2: Computational Methods (Izmailov and Solodov, 2007).