Optimization Concepts: Continuity, Convexity, and Stationary Points

Nov 27, 2023

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This chapter explores the basic concepts of optimization, including the continuity of objective functions in discrete cases such as insulation and pipe sizes, convexity and concavity of functions, stationary points as necessary conditions, comparison between quadratic and non-quadratic functions, and sufficiency conditions for minimization. FIGURE 4.9 showcases convex and nonconvex sets.

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Optimization Concepts: Continuity, Convexity, and Stationary Points

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Chapter 4 Basic Concepts of Optimization Chapter 4
Objective Function • issues: • continuity of f (discrete cases, e.g., insulation, • pipe sizes) • (2) convexity, concavity • stationary points (necessary condition) • quadratic vs. non-quadratic functions • scalar vs. vector case • (6) sufficiency condition (min) Chapter 4
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Chapter 4 FIGURE 4.9 Convex and nonconvex sets.
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