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2
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4

Jan. 30, Feb. 6, 13, 20 

MODULE 1:
Submodule 1.1: Equilibrium Problems, Motivation, Introduction, Background
-Introduction and simple examples for mixed complementarity problem/variational inequality problem (MCP/VI) formulations
-Review of nonlinear programming
-Theory behind KKT conditions for NLPs and how it relates to equilibrium problems
-Source problems

SUGGESTED READING (*= as needed depending on student's background)
(Gabriel et al., 2012):
Chapter 1
Chapter 2 (2.1-2.7 *)
Chapter 3 (Microeconomics*)
Chapter 4  (4.1)
Chapter 5 (5.1-5.3)

(Facchinei and Pang, 2003):
Chapter 1

(Cottle et al., 1992):
Chapter 1

HW 1 given out

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8
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10

Feb. 27 Mar. 6, Mar. 13, 27, Apr 3, 10

March 20-SPRING BREAK NO CLASS

Module 1:
Submodule 1.2: NCP/VI Engineering-Economic Models
Game Theory, MCP/VI, Two-Level Models
-Review of Game Theory Models: two-person zero-sum and bimatrix games (Minimax Theorem)
-Market Models: n-player games, equilibria in dominant actions
- Nash-Cournot Equilibria
- Generalized Nash equilibria
- Wardop traffic equilibria
- Spatial price equilibria
- Energy market equilibria: PIES, stochastic Nash power market, natural gas market

SUGGESTED READING: (Gabriel et al., 2012): Chapters 4,5,6,7,10, 11, 12 (as needed)

-Selected algorithms for equilibrium problems
SUGGESTED READING: (Gabriel et al., 2012): Chapters 8 and 9

-Selected existence/uniqueness results for MCP/VI (time permitting, we may come back to this area later in the semester)

Note:

2. Exam #1 date TBD

HW 2 given out

Apr. 17, 24, May 1, May 8

Module 2:
Mixed Integer Nonlinear Programming (MINLP) Problems , Motivation, Introduction, Background
- MINLP problem statement
- Two-level problems: MPECs, MPCCs (EPECs) as special cases
- Selected Methods to solve MPECs
SUGGESTED READING: (Gabriel et al., 2012): Chapters 8 and 9
- Other examples of MINLPs
-Generalized Benders Decomposition (GBD) and other approaches to solve MINLPs

SUGGESTED READING: (Floudas), Chapter 6 plus handouts

Note:
1. Exam #2 will be comprehensive but weighted more on the lectures after Exam #1
2. Exam #2 date TBD

HW 3 given out