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Optimization and Equilibrium Problems

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Weeks Topic (also see PowerPoint files for individual lectures for LINDO code or other relevant examples)
1&2
Problem classification, examples
•   "An Analytic Derivation of the Efficient Portfolio Frontier," R.C. Merton, The
    Journal of Financial and Quantitative Analysis, 7 (4), Sept. 1972, 1851-1872.
•   Min Cost Flow LP version 1 (min_cost_flow_v1.txt,   min_cost_flow_v1.xls)
•   Min Cost Flow LP version 2 (min_cost_flow_v2.txt,   min_cost_flow_v2.xls)
•   Portfolio optimization QP (portfolio_optimization.xls)
•   Haverly pooling problem (1978 and 1979 references -- see Blackboard site:
    https://bb.eng.umd.edu)
2
Some MATLAB basic commands
•   matlab_basics.m
3,4,5,6
 
7, 8, 9, 10
 
11-14
Algorithms for constrained and unconstrained problems
•   steepest descent example (steepest_descent.xls)
•   Newton's method example (newton.xls)
15
 

Sample Optimization Code:

Problem #1 (LP) Problem #2 (NLP) Problem #3 (QP)
MATLAB (fmincon)
MPL
XPRESS-MP/MOSEL
Excel (solver add-in)
LINDO
MATLAB (fmincon)
MPL
XPRESS-MP/MOSEL
Excel (solver add-in)
MATLAB (fmincon)
MPL
XPRESS-MP/MOSEL
Excel (solver add-in)

Optimization Software
(key:LP=linear programming, IP=integer programming,NLP=nonlinear programming, NCP/VI = nonlinear complementarity problem/variational inequality)

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