Non-Linear Programming Without Constraints

# Non-Linear Programming Without Constraints - UNC-Wilmington...

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UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas Consumer Choice with Non-linear Objective Functions Non-linear Programming with No Constraints Example Problems In this handout, we examine consumer utility maximization problems that can be classified as non-linear programming problems without constraints. Recall that if one or more of the equations in an optimization problem is non-linear, then we cannot use linear programming to solve the problem; instead, we must turn to non-linear programming. In the examples below, the objective function is a non-linear equation; this makes the problem a non-linear programming problem. When there are no constraints in a non-linear optimization problem, we are able to use " classical calculus " methods to solve the problem (as described below in this handout), and we do not need to use Lagrange's Method (the subject of the next handout) to solve the problem. On the other hand, when there are constraints in the problem, we cannot use classical calculus methods to solve the problems, and we must turn to Lagrange's Method. Example (1) * Nonlinear programming problem * One choice variable * No constraints (note: when we have no constraints, we DON'T need to use Lagrange's method) (note on the note above: Lagrange’s method is discussed in the next handout)

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## This note was uploaded on 10/22/2009 for the course ECN 321 taught by Professor Dumas during the Fall '08 term at University of North Carolina Wilmington.

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Non-Linear Programming Without Constraints - UNC-Wilmington...

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