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Optimization

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f(x) = 0 g i (x) = 0 h i (x) <= 0 Objective function Equality constraints Inequality constraints

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Terminology Feasible set Degrees of freedom Active constraint

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classifications Unconstrained v. constrained Linear v. non-linear Convex v. concave v. neither Continuous space v. discrete space

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Linear case Unconstrained makes no sense Simplex method Minimum at a vertex Start at a vertex, jump to adjacent vertex as long as objective is less Uses slack variables to turn inequality constraints Into equality constraints with variable: h(x) – s = 0;

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Non-linear unconstrained case Unconstrained makes no sense Simplex method Minimum at a vertex Start at a vertex, jump to adjacent vertex as long as objective is less Uses slack variables to turn inequality constraints Into equality constraints with variable: h(x) – s = 0;

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Lecture 8 – Nonlinear Programming Models Topics General formulations Local vs. global solutions Solution characteristics Convexity and convex programming.

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