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Multidimension Application Introduction and the Gradient

Excerpt

Many optimization applications have two or more decision variables. The previous chapters focused on univariate, one-DV, one-dimensional (1-D) applications. Although N-DV applications are more frequently encountered, univariate searches are important, and they reveal key issues in relatively uncomplicated situations. There are new issues and techniques associated with 2-D and higher-dimension applications, and this chapter begins a section related to 2-D, two-decision variable, and N-D applications. Each section of this book on optimization algorithms introduces techniques with 2-D examples and then extends the optimization techniques to N-D applications. In 2-D, we still have the generic optimization concept for maximization.

Many optimization applications have two or more decision variables. The previous chapters focused on univariate, one-DV, one-dimensional (1-D) applications. Although N-DV applications are more frequently encountered, univariate searches are important, and they reveal key issues in relatively uncomplicated situations. There are new issues and techniques associated with 2-D and higher-dimension applications, and this chapter begins a section related to 2-D, two-decision variable, and N-D applications. Each section of this book on optimization algorithms introduces techniques with 2-D examples and then extends the optimization techniques to N-D applications. In 2-D, we still have the generic optimization concept for maximization.

7.1Introduction
7.2Illustration of Surface and Terms
7.3Some Surface Analysis
7.4Parametric Notation
7.5Extension to Higher Dimension
7.6Takeaway
7.7Exercises
7.1Introduction
7.2Illustration of Surface and Terms
7.3Some Surface Analysis
7.4Parametric Notation
7.5Extension to Higher Dimension
7.6Takeaway
7.7Exercises

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