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Objective Function
issues:
(1) continuity of f (discrete cases, e.g., insulation, pipe sizes)
(2) convexity, concavity
(3) stationary points (necessary condition)
(4) quadratic vs. non-quadratic functions (5) scalar vs. vector case
(6) sufficiency condition (min)
0
i
X f
0
0
i
X f dX
df
0 H of s eigenvalue all
definite positive
0
2 2
H
Continuity of Functions
• In analytical or numerical optimization, preferable and more convenient to work with continuous functions of one or more variables than with functions containing discontinuities.
• Functions having continuous derivatives are preferred.
• The property of continuity
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FIGURE 4.9
Convex and nonconvex sets.
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Chapter 4
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Chapter 4