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A. Math Topics

A4. Solving Optimization Problems

How does one derive the solution to unconstrained/constrained maximization and minimization problems?


Video Description
a. General Structure of Optimization Problems (8:50)
(0:00) general structure of optimization problems
(0:46) world’s simplest optimization problems
(2:09) optimization problems with many control variables
(2:51) optimization problems with parameters
(4:05) optimization problems with constraints
(5:46) example: utility maximization
(6:38) example: cost minimization
(7:59) famous optimization problems in economics
b. Unconstrained Optimization (7:58)
(0:00) unconstrained optimization
(0:13) world's simplest optimization problems
(1:26) local vs. global maxima and minima
(4:06) economic example - profit maximization
(6:46) optimization with several control variables
c. Constrained Optimization (4:37)
(0:00) constrained optimization problems in economics
(1:00) tangency condition
(3:50) constrained maximization with n variables
d. Lagrangians (Calculus) (4:44)
(0:00) structure of constrained optimization problems
(1:45) first order conditions for constrained optimization
(2:25) method of Lagrangians to get the first order conditions
(3:35) setting partials of the Lagrangian equal to zero
e. Corner Solutions (7:01)
(0:00) maximization subject to a nonnegativity constraint
(2:35) interior solutions versus corner solutions