Chapter 1: Introduction and motivation
1.1. Introduction
1.2. Motivation
1.3. Optimization vs. complementarity problems: definition and characterization
1.4. Illustrative examples: of an optimization problem, equilibrium problem, optimization problem with equilibrium constraints and equilibrium problem with equilibrium constraints. 1.5. Exercises
Chapter 2: Optimality conditions
2.1. KKT conditions
2.2. Constraint qualifications for necessary conditions 2.3. Sufficiency conditions
2.4. Simple optimization problem (analytically solvable)
2.5. Simple optimization problem solved as an LCP or NLCP
2.6. Simple equilibrium problem (analytically solvable)
2.7. Simple MPEC (analytically solvable)
2.8. Simple EPEC (analytically solvable)
2.9. Nonconvex problems
2.10. Exercises
Chapter 3: Introductory microeconomic principles relevant for complementarity problems and market equilibria 3.1. Basics
1.1. Supply curves
1.2. Demand curves
1.3. Notion of equilibrium as intersection of supply and demand curves 3.2. Social Welfare Maximization
2.1. Definition of social welfare and associated optimization problem 2.2. Maximization of consumers' + producers' surpluses
3.3. Modeling individual players
3.1. Profit-maximization problem as paradigm
3.2. Perfect vs. imperfect competition
3.2.1. Price-taking producers
3.2.2. Monopoly
3.2.3. Oligopoly (Nash-Cournot, Bertrand games)
3.2.4. Cartel
3.4. Multi-level games 4.1. Stackelberg leader follower games (MPECs)
4.2. Multi-leader games (EPECs).
4.3. Nash vs. Generalized Nash equilibria
3.5. Exercises
Chapter 4: Equilibria as complementarity problems
4.1. Equilibria
4.2. Conditions involving primal and dual variables
4.3. Combination of equations and KKT conditions
4.4. LCP and Mixed LCP
4.5. NLCP and Mixed NLCP
4.6. Stochastic equilibrium problems
4.7. Formulation issues
4.8. Example: Electricity market equilibrium
4.9. Example: Gas market equilibrium
4.10. Exercises
Chapter 5: Variational Inequality problems
5.1. Variational Inequality (VI) formulation
5.2. VI vs. complementarity problems
5.3. Example of electricity/gas equilibrium
About the Author: Andy Sun is an assistant professor in the Stewart School of Industrial & Systems Engineering at Georgia Tech, USA. Dr. Sun conducts research in optimization and stochastic modeling with applications in electric energy systems and electricity markets. He also works on theory and algorithms for robust and stochastic optimization, and large scale convex optimization.
Antonio J. Conejo received an M.S. from MIT, US and a Ph.D. from the Royal Institute of Technology, Sweden. He has published over 190 papers in refereed journals and is the author or coauthor of books published by Springer, John Wiley, McGraw-Hill and CRC Press. He has been the principal investigator of many research projects financed by public agencies and the power industry and has supervised 19 PhD theses. He is an IEEE Fellow.